Can I choose which damage type my Sneak Attack does if my weapon does multiple types?

Question

Sneak Attack has the same type as the rest of the attack, this is easy, unless there are multiple damage types.

A Flame Tongue does slashing (or piercing) damage, and fire. Can I chose the Sneak Attack damage in this case to be fire too?

Answer 1

Maybe

First, Crawford did tweet under Sage Advice that

All Damage has a Type

This then leads us to the question of what damage type Sneak Attack should use.

In support of Primary type of damage

As you linked, Sneak Attack delivers damage of the primary type of the weapon (piercing, slashing, etc.)

The Flame Tongue states that it, (DMG, 170):

...deals an extra 2d6 fire damage...

emphasis mine

Jeremy Crawford also supports this with his Sage Advice answer:

QUESTION: Sneak attack has the same damage type of the weapon used?

ANSWER: That's correct

Therefore, the sneak attack damage of the Flame Tongue is that of the primary type of your flame tongue (whatever it may be) and NOT the fire damage.

In support of Choosing your damage type

Crawford suggests you may have a choice, though, in cases of multiple damage types

In another question about Hunters Mark Damage, Crawford answers somewhat differently:

Hunter's mark uses the same damage type as the attack that triggers it. If the attack has more than one damage type, choose one.

I don't think those two responses are at odds. You must use the damage type of the weapon, but if the weapon/strike delivers multiple damage types then you may pick. The Flame Tongue would give you that option for fire damage on Sneak Attack if you extrapolate this ruling on Hunters Mark to Sneak Attack.

Answer 2

RAW: There is nothing I can locate in the PHB or DMG to definitively say one way or the other. However, based on PHB 96:

Sneak Attack: 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...

I interpret this to mean that the extra damage as a result of a sneak attack comes from where the blow lands and that the opponent was temporarily distracted. As such, I feel it makes more sense for the extra damage to be piercing/slashing as opposed to fire, since the fire damage really doesn't care where the attack hits.

To put it another way, I view the progression as this:

1. Rogue hits a target dealing piercing/slashing damage under sneak attack conditions.
2. As a direct result of the hit, sneak attack damage is dealt.
3. As another result of the hit, Flame Tongue does 2d6 fire damage.

You can compare this to Dagger of Venom in the sense that the sneak attack is independent of the Con save leading to 2d10 poison. It wouldn't make sense for the sneak attack to potentially deal poison damage since the sneak attack damage occurs regardless of whether or not the Con save was made.

Answer 3

No, you don't get to choose

Contrary to the answer in the linked question, allow me to propose that Sneak Attack doesn't have a damage type because there is no type specifically mentioned in the text.

Not all damage needs to be typed

See this answer on the damage type caused by blood loss, as well as some in-universe examples of untyped damage: the Stirge's Blood drain, the Bearded Devil's Glaive, and the Horned Devil's Tail. Some types of damage in D&D is untyped and does not fit with the default types.

Sneak Attack only says you deal extra damage, without a type mentioned

The text for Sneak Attack says only this:

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.

You can reason out that, just as the blood loss over time does not have a well-defined type of damage, you can argue that the extra SA damage comes from the exploitation of the target's distractions and weak spots -- which is itself not a kind of well-defined damage.

Refutation of Jeremy Crawford's Tweet

This tweet claims that all damage has a type, given by Jeremy Crawford himself. This clearly shows the intent behind damage types. However, his tweet is directly contradicted by the Monster Manual, a core rulebook, by showing instances of damage that do not have a damage type.

Note that these instances are not mistakes because they are not in the errata. We are left with the designer stating design intentions that is contradicted by a core rulebook. The core rulebook is more authoritative than a tweet -- that's why it's a core rulebook.

Without JC's statement about all damage having a type, the viewpoint that some damage does not have a type is stronger.

Conclusion

You don't get to choose the damage type of Sneak Attack as it is an untyped damage on top of your normal weapon damage dice.