You’ll get an inordinate amount of pulp and other wood crap inside the saw. Chainsaws are designed to not allow this stuff to foul the mechanism and operation (though you have to empty the caked on stuff from time to time) but I can’t say whether your mitre saw would like it.
I bought a Husky 236e and found it to be an excellent and cheap little saw for branches and real tree felling alike.
Cutting branches on a mitre saw can be quite dangerous I have tried it. You need to be careful where the branch does not sit flat as the cut will cause the wood to bind on the blade generating serous amounts of kick back.