The Savage Attacker feat (PHB, p. 169) states:

Once per turn when you roll damage for a melee weapon attack, you can reroll the weapon’s damage dice and use either total.

Additionally, the rogue's Sneak Attack feature states:

Beginning at 1st level, you know how to strike subtly and exploit a foe’s distraction. Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.

Considering that Sneak Attack damage deals the same kind of damage as the weapon, would Savage Attacker benefit it and let you reroll the Sneak Attack extra damage dice?

No, it would not

The Weapon's damage dice is different from the total damage dice.

Savage Attacker works with allowing reroll on the weapon's damage dice.

Sneak attack and it's associated dice are a different mechanic and represent extra damage on top of the Weapon dice: it is not part of the weapon dice.

This makes sense from a rules perspective, but it also supported by Jeremy Crawford via Twitter:

Savage Attacker is meant to apply to the weapon's damage dice only

An example of language for when all dice are applicable

Critical hits are clear in their specificity to double all of the damage dice (emphasis mine):

Roll all of the attack's damage dice twice and add them together.

The wording here is clear in that all of the dice are to be rolled again and that it is applies to more than just weapon dice.