Can a creature with first strike kill a creature with deathtouch before it deals damage back?

Combat damage is dealt in two separate steps when first strike (or double strike) is involved. In the first combat damage step, only creatures with first strike or double strike deal their damage. Then, if any creatures with first strike or double strike are still in combat, a second combat damage step occurs for all remaining creatures (CR 702.7, CR 509.1–509.2).

Deathtouch means that any amount of damage that creature deals is enough to destroy the creature it damages (CR 702.2). However, deathtouch only matters when that creature actually deals its damage. If the deathtouch creature has neither first strike nor double strike, it does not deal damage until the second combat damage step.

So if a first strike creature deals enough damage to the deathtouch creature to destroy it in the first combat damage step, the deathtouch creature is put into the graveyard before the second damage step ever happens — meaning it never gets to deal its lethal (deathtouch) damage back (CR 510.2).

Example: A 2/2 with first strike blocks a 1/4 with deathtouch. In the first combat damage step, the first striker deals 2 damage to the 1/4, which is enough to destroy it. The 1/4 is removed before the second damage step, so it never deals its 1 damage back — the 2/2 survives unharmed.

Note that if the first strike creature does not deal lethal damage to the deathtouch creature in step one, the deathtouch creature survives to deal damage in the second step, and its deathtouch will then destroy the first striker.