Ok, very much at your own risk disclaimer here, as I have not seen the specific cables. If there's just 6 wires going to 6 pins, one-to-one, no cross-connecting or anything complicated, and the 6 pin is on the very end of the cable assembly; then conditionally yes, they should be able to be chopped off. There is a serious problem with that, however. You will be left with exposed conductors that must not be allowed to touch each other, the case, or any other components. I'm guessing there's 2 wires into 6 of the 8 pins for the 8 pin connector, one side back to the PSU and the other to the 6 pin connector. The exposed 12V there, after cutting them, could easily damage other components or start a fire if it shorts to ground; or the ground wires could short out something with voltage on it for the same result.
If you have the electrical knowledge and skills, it can be done safely. The fact that you're asking the question suggests that you maybe shouldn't take the risk. Don't leave them there with just air between them, and assume that no metal parts could fall on them, or similar. Whatever you do to insulate them needs to be secure and reasonably permanent/durable (e.g. just taping them up isn't great, as PVC electrical tape can come unstuck over time). Be careful not to damage the cables from the 8 pin to the PSU in the process.
A fresh set of cables with just the connectors you need is easier and safer, but has a cost. There's possibly an off the shelf kit from CableMod that might have suitable cables in it, or they do custom. Beware the PSU end of cables, the pinouts there are vendor-specific (not standardised), so you need cables that are compatible with your specific model/series of PSU.