You can report it but they will never find the perpetrator. It is a real shame and pretty infuriating.
However, I might be inclined to just forget about it. There is about zero chance of finding the guy who did it, and there is at least a small chance that the authorities become suspicious of you. I am not saying they have a reason to, I am just saying the LEOs are people and just like all other people some are good and some aren't. I tend to try to avoid contact with law enforcement unless it is necessary and/or there is at least a decent chance that they will catch the perp.
In reality, law enforcement isn't going to be fingerprinting deer carcasses or picnic tables, or taking molds of tire prints, over a few dead deer. It is a simple matter of resources and cost-benefit analysis. There is about a one in a million chance that they have some other evidence and your report will be the last piece of the puzzle they need. If it were me, that isn't enough for me to go through the headache and potential risk of contacting the law.