put someone out of his or her misery
.
Kill a wounded or suffering animal or person, as in
When a horse breaks a leg, there is nothing to do but put it out of its misery
.
[
Late 1700s
]
.
End someone's feeling of suspense, as in
Tell them who won the tournament; put them out of their misery
.
[
c. 1920
]
Both usages employ
put out of
in the sense of “extricate” or “free from.”