There is no hard reset on a video card. Everytime you reboot the computer the BIOS reinitializes the video card and transfers control to the video card's BIOS for its own post testing and initialization.
There may be some differences in video card initialization in a soft-boot vs. a power-down scenario, but I am not sure. In any case, if you power off the system, then power it back up, you've done all the hard resetting of the vid card you can do.
Oh, I assume you don't mean restoring BIOS settings in the vid card to their defaults. That's another subject, and you can usually do it in the drive control panel, though I am not expert on ATI hardware.