From the Victoria and Albert web site:
Concealed in the bodywork is a mechanical pipe-organ with several parts, all operated simultaneously by a crank-handle emerging from the tiger's shoulder. Inside the tiger and the man are weighted bellows with pipes attached. Turning the handle pumps the bellows and controls the air-flow to simulate the growls of the tiger and cries of the victim. The cries are varied by the approach of the hand towards the mouth and away, as the left arm - the only moving part - is raised and lowered.
Another pair of bellows, linked to the same handle, supplies wind for a miniature organ of 18 pipes built into the tiger, with stops under the tail. Its structure is like that of European mechanical organs, but adapted for hand operation by a set of ivory button keys reached through a flap in the animal's side. The mechanism has been repaired several times and altered from its original state. It is now too fragile to be operated regularly.
Here is a link to more on the history of Tippoo's Tiger.
Here is a link to a 26 minute video on Tippoo and a bit about the Tiger.
[ Thanks Falk! ]