DisplayPort can support a DVI passthrough. This would mean the DisplayPort end would have to be connected to your GPU. I've seen adapters for this purpose, but never a DisplayPort to DVI cable.
It seems more likely that you have a DVI to HDMI cable. The DisplayPort and HDMI connectors look similar. In that case, either way should work since HDMI and DVI-D are compatible up to 1920x1080 resolution at 60 Hz.
If either end of your cable is DVI, you won't get audio through this cable.