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

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

Emphasis mine. Savage Attacker causes you to reroll all of the weapon's damage dice, so if you used it with a greatsword that deals 2d6, you would reroll both dice and choose one of the two sets of results. In the same way, if something (such as a critical hit) causes you to roll the weapon's damage dice more than once, then you have the option of re-rolling all of those dice and choosing which to use.

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.