Tell me something: aren't semi-gods mortals? Of course, they are the sons of goodesses and that kind of stuff, but saying like that it looks like they can't die...

Do you mean demigods? If so, than no, they're not mortals, technically, but they can die. They are half god-half mortal, meaning they aren't fully mortal, but they can die because they are half mortal. The two aspects together actually makes it mais plausible that they'll die because they can be killed por celestial/imperial weapons, as well as steel and such.