I needed something similar for cutting a mesh in half. After trying all of the brushes, I found that Clay Strips is the cleanest, with little to no pushing in the back. It works for gouging out a surface just as well. These are the settings I used:
To save time, you'll want to adjust this depending on the level of detail and the radius of your brush. On average, this is the value I find works best in my case.
This setting is a necessity when trying to make any sculpt brush cut through a mesh, but it weakens the brush's effect on lower resolutions. In your case where you want to gouge, this isn't as important. But if you're trying to cut something in half, not using Autosmooth will take longer and cause backface clipping.
Sculpt Plane: Area Plane
Area Plane is much quicker than View Plane in this case. Also, keep the button next to this setting unlocked so the geometry can be carved properly.
Plane Offset: 0.000
The Clay Strips brush will need to act on whatever surface you use it on, without offset. Keeping this at 0.000 will help prevent distortion, and allow the geometry to be carved properly.
Front Faces Only: No
Like Autosmooth, Accumulate is another necessity for a cutting brush. It simply allows the stroke to continue without having to re-click, which is especially important here to save space in the undo history.
Stroke Method: Space