proc1.sh

#!/bin/sh
touch /tmp/proc1.signature.mutex
#do something for long time
sleep 100 
rm -rf /tmp/proc1.signature.mutex

proc2.sh

#!/bin/sh
touch /tmp/proc2.signature.mutex
#do something for long time
sleep 100 
rm -rf /tmp/proc2.signature.mutex

proc3.sh

#!/bin/sh
touch /tmp/proc3.signature.mutex
#do something for long time
sleep 100 
rm -rf /tmp/proc3.signature.mutex

core.sh

Now is there a way to wait for deleting /tmp/proc[?][*].signature.mutex all such file using loop or something
and then continue further execution

How to achieve objective of core.sh

A mutex is a mutual exclusive lock. Your procN.sh scripts never test whether the mutex is held by another process before "locking".

If you let core.sh start the other scripts, it would be easy for it to wait for the completion of them:

#!/bin/sh

./proc1.sh &
./proc2.sh &
./proc3.sh &

wait

# other processing

This removes the need for the lock files altogether. If that's not possible, consider

#!/bin/sh

while [ -e "$HOME/locks/proc1.signature.mutex" ] ||
 [ -e "$HOME/locks/proc2.signature.mutex" ] ||
 [ -e "$HOME/locks/proc3.signature.mutex" ]
then
 echo 'waiting...'
 sleep 10
done

# other processing

To avoid leaving files behind by the procN.sh scripts if they die of unnatural causes, use a trap:

#!/bin/sh

lockfile="$HOME/locks/proc1.signature.mutex"

while [ -e "$lockfile" ]; do
 echo 'Can not get lock. Waiting...' >&2
 sleep 10
done
## alternatively:
# [ -e "$lockfile" ] && echo 'something is wrong' >&2; exit 1; 

trap 'rm "$lockfile"; exit' EXIT INT TERM HUP
touch "$lockfile"

# etc.
# no need to rm the lock file at the end

Note that there is a space between the -e "$lockfile" test and the touch in which another process may lock the same file.

To avoid this, use a lock directory instead:

#!/bin/sh

lockdir="$HOME/locks/proc1.signature.mutex"

while ! mkdir "$lockdir"; do
 echo 'Can not get lock. Waiting...' >&2
 sleep 10
done
## alternatively:
# [ -e "$lockdir" ] && echo 'something is wrong' >&2; exit 1; 

trap 'rmdir "$lockdir"; exit' EXIT INT TERM HUP

# etc.
# no need to rmdir the lock dir at the end

You may also use a symbolic link in a similar way.

Note that I've used a path under $HOME for the lock files/directories. If using /tmp, any user could potentially lock your script out of action by simply creating the correct file/directory.