The past tense of put somebody out of (his or her) misery is also put somebody out of (his or her) misery.

The third-person singular simple present indicative form of put somebody out of (his or her) misery is puts somebody out of (his or her) misery.

The present participle of put somebody out of (his or her) misery is putting somebody out of (his or her) misery.

The past participle of put somebody out of (his or her) misery is put somebody out of (his or her) misery.