It still makes a bit of a strong point
He could had the minister totured
made to swear alliegence at gun point
or even step down
but no he decides to obliterate him with a mortar round
He is afraid too, if he let the minister live, someone with the power of the army, things could go south for him very quickly especially if he made the guy resentful through torture or force alliance. I read enough history to know normally only three things happens in this situation: 1) The one serving is killed to ensure ruling party's power 2) The serving party is wise enough to know when to step down and request to leave the position of power hence avoid death 3) The serving party actually do have the ambition to take over and did so successfully.
So yeah death is what I would've done in his situation, it's cruel but I rather keep my own life than saving his.
And about the replacement, normally ruling party will choose someone he can trust, not someone from the previous generation, I don't think I ever heard of replacement actually try anything in history but I could be wrong.