The Tavern

For a human Arcane Marksman, are potions of mutation worth playing with? seems more downside than up.

It mostly depends on the number of mutation potions you have. Mutation potions are biased toward good effects. Generally the higher number of mutation potions you have in the early game, the more correct it is to quaff as it could provide a significant boost in power to allow you character ahead of the power curve. Generally, it is best to save most mutation potions for the bad mutations you get throughout the game. There are several bad mutations - the worst are the ones that teleport you, berserk you, or give your blurry vision. If you get any of these throughout the game, you should quaff mutation to get rid of it. The other bad mutation that could be worth losing would be frail.

For any combination, they are worth playing with. It is risk of course, but the more potions you have, the more times you can roll the dice to get a set of positive ones, and/or remove any negative ones you just received. The primary reason to not use them is to save them for when you receive bad mutations via malmutate, as a means to attempt to improve your condition.

Since I run out of space, and had no clue how to use them, I usually just dropped them off. Die and learn as they say.

The correct way to use them is to drop them when you run out of space, and come back for them if you get mutated in a way that's badly to your disadvantage (blurry vision, berserkitis, teleportitis are all potential game-enders)

Later, It might be worthwhile to carry them into parts of the extended game where it's likely you'll be mutated and you won't be able to easily auto-travel back for them (notably pan)

It's rare, but If I get a stack >10 or so and I'm feeling particularly cheeky, I might drink one to spice up my game, but that's not a winning strategy, it's just something to do when you've played thousands of games and just want to see something different.

If you usually don't make it to Zot, and you want to learn the game, I'd suggest quaffing some !mut sometimes.
If you get to the point were you often make it to Zot, you'll probably usually want to put your mutation potions in a stash.
(Because I almost never run out of Mutation potions before Zot.)