If I use Deathgrip, can I use it to kill a card in my hand?

No, you cannot use Deathgrip to kill a card in your hand.

According to Rule 428.1, a "Kill" action refers specifically to a permanent moving from the board to the trash. Furthermore, Deathgrip specifically targets a "friendly unit." Cards in your hand are not considered units on the board, so they are not valid targets for Deathgrip.

As established in RiftJudge FAQ #9295 and RiftJudge FAQ #9315, you must choose a valid, friendly unit currently on the board as a target at the moment you play Deathgrip and place it on the chain.