Walkers found the bird of prey caught in a metal spring trap on moorland near Winscar Reservoir, in the northern Peaks near Penistone.
The buzzard was taken to a local veterinary practice, but its injuries were so serious it had to be put down.
The species is protected by law, and trapping the birds carries a maximum fine of £5,000 or six months in jail.
Spring traps can be used lawfully to catch stoats and weasels, but must be set in tunnels to avoid hurting birds.
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Geoff Nickolds, chair of the Peak District Birds of Prey Initiative, said: “The death is especially upsetting as the bird had been ringed as a chick last year at a nearby site.”
n Call 101 or Crimestoppers on 0800 555 111 with information.