You can say shot to death. It is used often.

You totally can though. It's a common phrase.

If you read American news, you'd see "shot to death" used frequently.

You can be shot and not die, btw.

Do you mean peculiar or is this a word I don't know (not native speaker).

You can be bored to death and amused to death, too.

What you can't say is "somebody was murdered to death".

You can, and people / publications do all the time. You need to read more.

"boy found shot to death in Northwest Side street"

"shot to death inside NYC public housing "

"Franklin man shot to death"

All from recent headlines.