You can delete geometry in 3d edit mode either by:
- Hiding all but the geometry you want to keep, and using the “delete hidden”, function. (Your mesh will need to be at the lowest level of subdivision).
Hint: to keep smoothing from being applied, and losing some high resolution detail on the remaining mesh, apply “mask all” to the visible mesh right before using “delete hidden”.
or
- Hide all but the geometry you want to keep, and use the “split” function in the subtool menu to split it off into its own subtool, then delete the subtool.
The only reason why you 'd want to do #2, is because for very dense, complicated meshes with many levels of subdivision, occasionaly deleting partial geometry at the lowest level can result in crashes, which deleting via the second method avoids.
In 2D mode simply use the “eraser” tool to erase portions you dont want.