The workflow that has gotten into my fingers when the gloss engine is causing trouble, for whatever reason, is to just make a cross: start with no connection, extend the track from the top all the way to the bottom, and from the right all the way to the left. At the intersection Altium will break both tracks, and you can delete the unwanted pieces. This is a little more useful when 45 degree angles (or worse) are involved, but it's a good tool for your toolbox regardless.
Note if you are doing this with copy-paste, you'll need to place another track continuing one of the ones you want broken (or just in the same area? I can't tell) before Altium notices what you're up to and actually does the split at the intersection. It's clunky to explain but will become obvious if you try to do it.