How Do I Remove the Wires from My Graphics Card?

Looks like you've got a liquid cooled GPU there. The hoses and radiator need to come out as a whole unit; you can't just detach those wires. So yes, you'll have to remove the entire assembly.

Those wires aren't regular cables; they’re actually hoses for a liquid cooler. You need to remove the entire radiator since it's attached to the GPU. Be careful, as opening it up will cause the fluid to leak out.

To process this smoothly, just remember that you need to remove both the fan and the radiator. They are stuck to the GPU, so taking them out together is the way to go.