The feral cat was found with a front foot caught in the spring trap in Durran near Castletown, Caithness, on 10 December.
The Scottish SPCA said the extent of the injuries to the bones in its paw caused the cat a "great deal of pain and suffering".
The charity believed the trap to have been "poorly or illegally" set.
A vet advised that the animal should be put down.
The SSPCA said: "Spring traps can be used lawfully under specific conditions for trapping small mammals such as rats, stoats and weasels. They have to be covered over, secured and prevented from catching any non-target animal.
"The fact that the cat was caught by his paw strongly suggests the trap was set either illegally or extremely poorly.
"We would appeal to anyone with information about who may have set the trap to contact us in confidence."
A cat has had to be put down after being badly injured in a trap used for killing rats, stoats and weasels.