You either have 1 very fast dog, or that deer was injured or sick, imo. When I was a kid, I used to watch from the loft of our barn as our collie dog chases deer , and he never even managed to get close to one. I’d say it was the same deer the second time, and he had some kind of problem that would have made him fall victim to any of several predators. In short, you’ll never cure the dog of wanting to kill deer. But the deer will cure the problem by not being slow enough for him to catch, usually.
I can’t imagine a border collie going toe-to-toe with a deer and not needing at least some stitches.
Attacked by the mut while snoozing in the brush
Just pray that the dog doesn't transfer it behavior over to your neighbors calves, sheep, goats or fowl. The neighbors will then solve the problem with extreme prejudice with justification and may even present you with a bill plus be pretty perturbed at you for some time.