Instead of placing the shape (to subtract) on areas to remove, you would place the shape on areas to keep, simply make the shape go around the rest of the line and not the tip you want to remove)
You can quickly and easily do this by just making choppy lines with the pen tool, but that may end up messing with alignments etc.
If you're not worried about those kinds of things, and all you want is the speed/efficiency, this is the way to go.
If you prefer a more proper method (will take a bit more time) and pretty wasteful for this simple shape. It can be useful for complex artwork (Since clipping masks are non destructive), but in this scenario it's a waste - once you're already cutting the path and going through the whole effort...
clone the line path (Ctrl+C / Ctrl+F) and expand it (Object → Expand)
Now carefully make the pen strokes where you want them (make sure to align them with the edges of the expanded path) and then use the Shape Builder Tool (Shift+M) to separate them and delete the part you want cut off, now go ahead and make the clipping mask.