ASUS A68HM-K and gtx 1070?

Solution
Compatible yes but whatever CPU you have running on that board is nowhere near strong enough to make use of a 1070.

Even the 880k (which is the strongest FM2+ CPU available) would be lucky to make 50% usage of a 1070.
No , you can use a 1070 now but its an expensive card & wasteful money wise.

It would be like having a Ferrari that's stuck in second gear.

Unless you're running at least 1440p or maybe even 4k resolutions its not a sensible buy.
For 1080p its absolute overkill.