Quote ( I have read and seen numerous times that when a deer shot in the main part of the body 'drops on the spot' it is due to the bullet striking too high and causing a shock to the spine. Then, very often, the deer will get up and run away. end of quote)
Answer to your question snowstorm:

When the bullet strikes the deer 2 events take place same time.

1. You have a slow incapacitation mechanism ( damage leading to knockdown ). All this means is the bullet creates a hole (Wound) destroying tissue in the path of the bullet. Due to hydrostatic pressure around this wound you get bleeding, bruising etc (meat damage). Sufficient damage dead deer, takes time to bleed.

2 You have fast incapacitation mechanism (knockdown). This second event is due to ballistic pressure waves going through the body affecting the brain ( knockout as per boxers) unconsciousness ,falling recovery and running off. if no 1 not immediately fatal.

Researchers have measured the size of these waves which are related to the kinetic energy (KE) of the bullet ( 1/2 weight of bullet times square of velocity divided by depth of penetration )So obviously as it goes through the deer the longer in the body it transfers more of this energy to the deer. So a non immediately fatal shot this can play a part, in knockdown and recovery