This is what the dictionary defines harvest as........

1. The season for gathering in agricultural crops
2. The act or process of gathering in crops
3. A mature crop
4. An accumulated store or productive result

A crop is defined as (as it relates here)

2. A plant or animal or plant or animal product that can be grown and harvested extensively for profit or subsistance.


So the way I see it is.........

If a person is raising deer specifically for profit, such as a high fence preserve, then the deer are harvested.

If a person is specifically raising deer for food such as on a farm, like cows or pigs, then the deer are harvested.

If a person goes and takes an animal from the wild that they kill that animal.