There are two “bites” during tiger mating. I will quote verbatim the account by the former director of the Delhi Zoo, Kailash Sankhala, of a mating encounter between tigers. It explains and refers to the two bites (highlighed).
“The tigress “kisses” the tiger – bites him gently – turns, rubs her body against his, raises her tail, and finally presents herself by sitting with forelimbs fully extended and hind-legs more than half-bent. The tiger mounts her in a half-knees bent position without putting any pressure on her body and she admits low, deep “Oaar oaaa” sounds. As the act comes to a climax, the tiger lowers his head and grips the skin folds of her neck firmly but carefully; this position helps both to achieve proper orientation at the time of the climax. The tiger then gives the peculiar high-pitched squeal…, The tigress growls, and finally gives a sudden jerk to dislodge the male. She turned round to face the tiger and start boxing.
This is a quote reproduced in the book Wild Cats of the World by Mel and Fiona Sunquist. The quote comes from the book by Sankhala KS of 1977 called Tiger: The story of the Indian tiger published by Simon and Schuster, New York.
I am indebted to the authors referred to. I believe that the quote fully explains why tigers bite during mating. I think the question actually is meant to refer to the male tiger biting the female. This is not quite a bite more the maletiger gripping the female and the reason is enlightening. On my reading of it, it ensures that the male tiger is able to insert his penis accurately. How about that!
P.S. We see the same or similar behaviour with male domestic cats when mating. And you will see the same with lions. There is one last point to make, in retrospect, which is that when the male cat “bites” the female it does help to maintain a dominant position and stop the female from swiping at the male. That applies with domestic cats and may well apply to tigers.