This mouse was very much alive. No doubt there was a right thing to do. Whatever it was, I didn't think of it. Instead I got a long knife and tried to skewer him with it. This was not notably successful.
Mice can move very fast.
Frightened mice can jump very high. Out he pops, dashing all over the kitchen at remarkable speed, until he finds his hidey-hole. I rebaited the trap and set it out again in an enticing spot. Surely this little creature will have learned from experience and will not be taken in again by free peanut butter. So it seemed for several days - nights actually for mice are nocturnal creatures.