Because it reminds him of Aerys, and look what happened to Aerys.
I would also like to submit that Tywin is not at all impulsive, and whether or not he’s a sadist is debatable.
Tywin tended to give his actions due consideration and think them through. This didn’t mean he didn’t make bad decisions but they weren’t hasty ones at all. And I have a hard time seeing Tywin decide to hurt people just because he gets off on hurting people; Tywin at least understands that you have to treat your leal bannermen and to an extent defeated foes with a modicum of protection, respect, mercy, and even largesse.
Put it another way: Tywin, after the Battle of the Blackwater, offered pardons to many of Stannis’ supporters and accepted them back into the King’s Peace quite happily. He does this because he doesn’t have an inherent need to hurt them, and because he understands the politics, history, and context of the situation and has considered them carefully.
Joffrey, had he been the one in charge, would probably have staged a grotesque mass execution for no better reason than that he gets off on watching people get hurt, especially if he’s the one doing the hurting. He wouldn’t have bothered to think beyond that at all.
I don’t think Tywin is immune to acts of violence carried out for emotional reasons as opposed to mere statecraft – a lot of what he did in the Rains of Castamere was personal not business, likewise despite his claims I’m pretty sure he wanted Elia dead for having gotten in between Cersei and Rhaegar, plus there’s what he did to his father’s mistress and to Tyrion and Tysha.
But there is a difference when it comes to self-control. Tywin does nothing indiscriminately or in hot blood, he makes sure that his acts of personal satisfaction also serve his larger political interests, and when he does lash out he does so because he wants to hurt specific people for specific reasons, not because he enjoys hurting people in general.
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