You generally can't dig all the graves you come across, only special ones. All the places in the game where you can dig have a similar patch of dirt, so just click when you're near the dirt patch and he'll start digging.
The first place you come across where it's possible to dig is the bandit camp. I've found three places there:
1. Near the fire where the workers are sitting originally.
2. Near the "Disgusting Moths" (or where they were before you killed them).
3. A little beyond that same place, near the chest along the mountain side.
You can try it out there so you know what to look for.