I made an ice cream for Thanksgiving dessert, but it came out painfully sweet. Can I melt down and rechurn with less sugar?

Make another batch (or 1/2 batch) of under-sweetened ice cream and blend them together while softened.

Or, as Phil says, depending on the flavor, mix with some soft cheese (cottage, mascarpone, cream, even feta) to make an ice cream pie or cheesecake.
Optional cookie crust of complementary flavor.
The cheese will cut the sweetness.
You can then add (either when mixing for freezing) your favorite garnishes - chocolate, fruits, nuts, whatever.

What Flavor is it? Depending on the flavor, I would let it soften a bit then mix in some espresso (unsweetened) and maybe some dark chocolate chips of chunks, then put back in the freezer. Espresso chip ice cream! You can even do a small test cup and see if it works.

You can rechurn a base after you've let it melt, but you'll need to make sure there's still enough sugar that the base churns into an ice cream. Depending on the flavor of your ice cream, you could also consider adding a savory topping (like aged balsamic, flaky salt, bread crumbs, or olive oil) or mixing it into a milkshake to offset the sweetness.

Hey there—we've melted and re-churned ice cream before with limited success (the texture isn't quite the same, though it does work), but I wouldn't do this if you're looking to alter the sweetness. Best to start again, and/or change this too-sweet version into something else: Mix it into a quickbread, for example, or serve milkshakes (with added yogurt, perhaps, to cut the sweet) for dessert? That'd be a story, at least?!