Jake (Dr. Dolittle)

From Muppet Wiki

Jake is the star tiger at Blossom's Mammoth Circus in Dr. Dolittle. Plagued by headaches, nauseau, and double vision, the troubled Jake decides to commit suicide by leaping from a bell tower. John Dolittle is informed of the tiger's plight, and sets out to help him (although a stay in a mental institution briefly deters him). Dolittle brings Jake to his hospital and succeeds in performing a vital, life-saving operation.

The animatronic Jake was used for every shot in the climactic surgery scene, with a live tiger used in all other on-screen instances.