As others have said, this is an easy push preflop. The guy is stealing from BTN, he only has 14BB, and the guy behind you has even less. If you are not going to push, then the second best option is to fold. Calling from SB with a bad hand like A8 offsuit is the worst option preflop.
On the flop you have nothing going on other than some backdoor draws, so just giving up would be perfectly acceptable. It is a low board, which he has missed a lot though, so a sizable donk bet (leading out) or a check-jam could also be an option. Instead you made a check mini-raise, which is pretty much the worst of any options available, since you are just massaging the pot larger, when you are out of position with absolutely nothing.
You want him to fold here, and the way to make him fold is to put his tournament life at risk, not by making it very cheap for him to stick around. With this hand he would likely have called and won most of your chips, but that is ok. Turbo tournaments are high variance, and you cant do well in them, if you are always afraid to bust. When its down to BTN vs. blinds or blind vs. blind, and someone has a better ace or a better pair than yours with stacks this short, its basically just a cooler.
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