mjhjmtu

Assuming in a presentation first a large and relatively complicated tikzpicture is shown. After this overview, the focus should be set to two small parts of the graph and next to it, there should be a ennumeration, describing the relevance of these two subprocesses. I've tried the following using the spy tikzlibrary:

usepackagetikz
usetikzlibraryspy

begindocument
 begintikzpicture[spy using outlines=rectangle, magnification=5, size=2cm, connect spies]
 defcorxb0
 defcoryb0
 %firstly defining the start variables so the object can be positioned relatively to another object.
 %fill the tank with water
 fill[top color=blue!90!,bottom color=blue!2,middle color=blue!30,shading=axis,opacity=0.15] (corxb,coryb+4) circle (2cm and 0.5cm);
 fill[left color=gray!50!blue,right color=blue!50!black,middle color=gray!50,shading=axis,opacity=0.15] (corxb+2,coryb) -- (corxb+2,coryb+4) arc (360:180:2cm and 0.5cm) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm); 
 %draw densely dashed lines for the "hidden" lines
 draw (corxb-2,coryb+0) arc (180:0:2cm and 0.5cm);
 draw (corxb-2,coryb+4) arc (180:0:2cm and 0.5cm);
 %draw the outline
 draw (corxb-2,coryb+4) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm) -- (corxb+2,coryb+4) ++ (corxb-4,coryb);
 draw (corxb-2,coryb+4) arc (180:360:2cm and 0.5cm);

 spy [red,dashed, magnification=1.8] on (-1.5,0) in node at (-2,-2);
 spy [red,dashed, magnification=1.8] on (1.5,0) in node at (2,-2);
 endtikzpicture
enddocument

This is fine as it is, but it doesn't allow to add bullet points to describe the graph. Therefore, I want to display only the magnified part, while having the enumeration as described above (the enumeration is not directly related to this question, however, I thought I'll leave it in to describe my intentions):

Additional clarification: i only need the magnified part, there is no need for the rest of the graph to be displayed.

A possiblity seems to be to just clip the picture, but i think it's quite impractical to do especially if you're working with large graph that have different elements and you don't know exactly where a certain node is located exactly e.g. in the case of (nodeX.south).

documentclassstandalone
usepackagetikz
usetikzlibraryspy

begindocument
 begintikzpicture[spy using outlines=rectangle, magnification=5, size=2cm, connect spies]
 path[clip] (-2.25,-1) rectangle (0,0.75);
 draw[red, thick, dashed] (-2.25,-1) rectangle (0,0.75);
 %
 defcorxb0
 defcoryb0
 %firstly defining the start variables so the object can be positioned relatively to another object.
 %fill the tank with water
 fill[top color=blue!90!,bottom color=blue!2,middle color=blue!30,shading=axis,opacity=0.15] (corxb,coryb+4) circle (2cm and 0.5cm);
 fill[left color=gray!50!blue,right color=blue!50!black,middle color=gray!50,shading=axis,opacity=0.15] (corxb+2,coryb) -- (corxb+2,coryb+4) arc (360:180:2cm and 0.5cm) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm); 
 %draw densely dashed lines for the "hidden" lines
 draw (corxb-2,coryb+0) arc (180:0:2cm and 0.5cm);
 draw (corxb-2,coryb+4) arc (180:0:2cm and 0.5cm);
 %draw the outline
 draw (corxb-2,coryb+4) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm) -- (corxb+2,coryb+4) ++ (corxb-4,coryb);
 draw (corxb-2,coryb+4) arc (180:360:2cm and 0.5cm);

 %spy [red,dashed, magnification=1.8] on (-1.5,0) in node at (-2,-2);
 endtikzpicture
enddocument 

You mean something like this:

documentclassstandalone
usepackagetikz
usetikzlibraryspy


begindocument
 begintikzpicture[spy using outlines=rectangle, magnification=5, size=2cm, connect spies]
 defcorxb0
 defcoryb0
 %firstly defining the start variables so the object can be positioned relatively to another object.
 %fill the tank with water
 fill[top color=blue!90!,bottom color=blue!2,middle color=blue!30,shading=axis,opacity=0.15] (corxb,coryb+4) circle (2cm and 0.5cm);
 fill[left color=gray!50!blue,right color=blue!50!black,middle color=gray!50,shading=axis,opacity=0.15] (corxb+2,coryb) -- (corxb+2,coryb+4) arc (360:180:2cm and 0.5cm) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm); 
 %draw densely dashed lines for the "hidden" lines
 draw (corxb-2,coryb+0) arc (180:0:2cm and 0.5cm);
 draw (corxb-2,coryb+4) arc (180:0:2cm and 0.5cm);
 %draw the outline
 draw (corxb-2,coryb+4) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm) -- (corxb+2,coryb+4) ++ (corxb-4,coryb);
 draw (corxb-2,coryb+4) arc (180:360:2cm and 0.5cm);

 spy [red,dashed, magnification=1.8] on (-1.5,0) in node at (-2,-2);

 draw (0, -1.3) node[text width=3cm, text height = 1cm] 
 beginitemize
 item M1
 item M2
 item M3
 enditemize
 ;
 endtikzpicture
enddocument 

to get:

Note that I just removed another panned out view just for avoiding redundancy.

Update 1: I have removed most of the parts of the plots as the OP wanted. However, the part that OP wants to remove remain unaffected. May be there is better way to achieve that.

documentclassstandalone
usepackagetikz
usetikzlibraryspy


begindocument
 begintikzpicture[spy using outlines=rectangle, magnification=5, size=2cm]
 defcorxb0
 defcoryb0
 %firstly defining the start variables so the object can be positioned relatively to another object.
 %fill the tank with water
 fill[top color=blue!90!,bottom color=blue!2,middle color=blue!30,shading=axis,opacity=0.15] (corxb,coryb+4) circle (2cm and 0.5cm);
 fill[left color=gray!50!blue,right color=blue!50!black,middle color=gray!50,shading=axis,opacity=0.15] (corxb+2,coryb) -- (corxb+2,coryb+4) arc (360:180:2cm and 0.5cm) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm); 
 %draw densely dashed lines for the "hidden" lines
 draw (corxb-2,coryb+0) arc (180:0:2cm and 0.5cm);
 draw (corxb-2,coryb+4) arc (180:0:2cm and 0.5cm);
 %draw the outline
 draw (corxb-2,coryb+4) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm) -- (corxb+2,coryb+4) ++ (corxb-4,coryb);
 draw (corxb-2,coryb+4) arc (180:360:2cm and 0.5cm);

 spy [red,dashed, magnification=1.8] on (-1.5,0) in node at (-2,-2);

 draw (0, -1.3) node[text width=3cm, text height = 1cm] 
 beginitemize
 item M1
 item M2
 item M3
 enditemize
 ;
pgfresetboundingbox
path[use as bounding box, draw=none] (-3,-3) rectangle (0,-1);
 endtikzpicture
enddocument

which would give you:

Here I reset the bounding box to achieve this much. However, I believe with overlay much more can be achieved.

Update 2: Now achieved without the usage of spy. Considering the OP only needs a part of the figure to be displayed, usage of spy doesn't make much sense per se.

documentclassstandalone
usepackagetikz


begindocument
 begintikzpicture
 defcorxb0
 defcoryb0
 %firstly defining the start variables so the object can be positioned relatively to another object.
 %fill the tank with water
 fill[top color=blue!90!,bottom color=blue!2,middle color=blue!30,shading=axis,opacity=0.15] (corxb,coryb+4) circle (2cm and 0.5cm);
 fill[left color=gray!50!blue,right color=blue!50!black,middle color=gray!50,shading=axis,opacity=0.15] (corxb+2,coryb) -- (corxb+2,coryb+4) arc (360:180:2cm and 0.5cm) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm); 
 %draw densely dashed lines for the "hidden" lines
 draw (corxb-2,coryb+0) arc (180:0:2cm and 0.5cm);
 draw (corxb-2,coryb+4) arc (180:0:2cm and 0.5cm);
 %draw the outline
 draw (corxb-2,coryb+4) -- (corxb-2,coryb) arc (180:360:2cm and 0.5cm) -- (corxb+2,coryb+4) ++ (corxb-4,coryb);
 draw (corxb-2,coryb+4) arc (180:360:2cm and 0.5cm);
 % you really don't need it if you only want to display a part of the whole
% spy [red,dashed, magnification=1.8] on (-1.5,0) in node at (-2,-2);
draw[red, dashed] (-2.05,-0.55) rectangle (-.95,0.55);
draw[fill=white, draw=none] (-.95,0.55) rectangle (.15,-0.55);
 draw (1, 0.2) node[text width=5cm, text height = 1cm] 
 beginitemize
 item M1
 item M2
 item M3
 enditemize
;
%draw[fill=red, draw=none] (-2.05,0.55) rectangle (.15,-1.45);
pgfresetboundingbox
 path[use as bounding box, draw=none] (-2.05,0.55) rectangle (.15,-1.45);
 endtikzpicture
enddocument

this will give

This is done by hard-coding the bounding box atop the desired area.