Depends if it's built in or downloaded. For downloaded assets, find the asset in content manager and delete it. Start Trainz, edit the route, click Menu, Delete missing assets.
If it's built in you can't delete it from content manager, so the workaround for that is to find a similar object that is not built in - download one if you need to. In surveyor, click Menu, Replace assets, then select the sign you want to get rid of and drag the text across to the replace window. Find the asset you want to replace it with, drag that across to the replace with window. Save, exit, back to content manager, delete the asset you just replaced the built in one with. Repeat as above, delete missing assets and they're all gone.