With damage to two sides of the trunk, unfortunately, I think your tree will be, at best, severely compromised if it does survive.  It would be best to replace it now as fall is a good time to transplant trees and you will be surprised how quickly a new tree will grow once it settles in.  proper planting and aftercare are critical as well as protecting your new tree from deer damage.

 An excellent resource for installing new trees:

https://www.extension.purdue.edu/extmedia/fnr/fnr-433-w.pdf

Below are two good websites with information on deer rubbing damage.

https://www.uidaho.edu/-/media/UIdaho-Responsive/Files/Extension/topic/nursery/diseases/deer-antler-rubbing.pdf?la=en&hash=CCC5F57E40E50A70DE05732983A2AB4808C18F65

An excerpt:

"If the injury is only on one side of the tree, the tree has a good chance of survival, although it will be weak in that spot, and have an ugly scar. If the injury is all the way around the tree, it will most likely die."

https://www.johnson.k-state.edu/lawn-garden/agent-articles/miscellaneous/deer-damaged-trees.html

An excerpt:

Bucks like to rub their antlers on young trees, causing extensive damage to the bark, which often results in a slow death for the tree. Protecting trees from damage is essential in areas populated with deer. Unfortunately, once the damage is done, there is little that can be done to repair the tree. Most times, the tree will need to be removed. I recommend protecting all trees, deciduous and evergreen, under 6 to 8 inches in trunk diameter."