Yes. You will need another PSU. That is unless you were to have a couple of SATA splitters, then SATA->molex converters, then molex to 6-pin connectors! LOL. But I believe the HD7750 doesn't require an extra connector?
I'm not using any splitters/adapters in my pc. I use whatever comes from the PSU! I have one HDD that uses the SATA power connector and it comes directly from the psu. In fact, the 2 SATA connectors come out seperately from the rest. The only adapter I would use would be the 2 molex to 1 6-pin pci-e connector.