Tigers eat deer as they would any other large prey animal. They normally kill large prey animals with a throat bite which is maintained for several minutes or longer until the animal has suffocated and dies. They make sure that the animal is dead by holding the bite beyond the moment the prey animal stops struggling. They take their prey into cover before beginning to eat.
They normally start feeding on the rump or buttocks. As they progress during the meal they open the body cavity and remove the stomach. They put the stomach to one side and then drag the carcass a short distance before continuing to eat it.
Tigers normally eat in a prone position resting on their elbows. They use their carnassial teeth, which are their molars, to slice the flesh. The molars of a cat are like scissors rather than like human molars which grind the food because the crown is flat. Tigers’ molars slice off large chunks of meat. They use their tongue which is like a domestic cat’s; covered in sharp, keratin spines or papillae to shred the flesh from the bones.
They sometimes grasp a bone between the front paws to keep it still while they eat. They might place a paw on top of a chunk of food while tearing pieces off it. Occasionally they use the paws of their forelegs to handle the flesh.
They normally eat and then rest and then restart eating. They lie close to the carcass until most of the edible parts of it have been eaten.
In Chitwan, a tigress spent three days, on average, with each of her large kills. She consumed an average of 46 kg of meat each time.
Tigers will usually cover the remains using rocks, grass, dirt or leaves if they have to leave the carcass to drink or find a rest site.
Over several days of feeding the carcass may be dismembered and the bones scattered.
Small prey animals are eaten quickly. Animals the size of a barking deer or young chital, weighing about 20 kg, are eaten at a single sitting.
Research indicates that an adult tiger consumes 18 to 27 kg of food in a night. I have a page on how much food a tag eats during the day which you can access by clicking this link here.
Reference: Wild Cats of the World (strongly recommended) and myself. If you’d like more detailed references please ask in a comment.
P.S. Tigers in Royal Bardia NP, Nepal often eat hog deer and in the Huai Kha Kharng Wildlife Sanctuary in Thailand tigers often eat barking deer.