Only HDMI 2.0 supports refresh rates higher than 60hz at resolutions higher than 1080p; up to the 1.4 standard, you're getting a max bandwidth consisting in images of a 1080p resolution 60hz plus audio signals, period.
That doesn't mean you can't go higher at all, but you need to balance things out. AFAIK you can't take out audio, but you can increase refresh rate above 60hz if you lower the resolution, or viceversa you can increase the resolution above 1920x1080 if you lower the refresh rate. For example, 4K-HD can be achieved if you set a 30hz refresh rate.
If your monitor and your gpu support HDMI 2.0, then there's no reason in getting a DisplayPort cable. After that short explanation, however, there's no reason in buying a DisplayPort cable either unless you plan on transferring audio with it. A DVI-D Dual Link cable will work exactly like a DisplayPort, but without transferring audio...