I don't think there is a one button clears all solution but you can do it one by one.
Hover your mouse over a skill then right click a skill, drag the mouse anywhere off the skill bar, and then release the mouse button and that should clear that skill. Rinse and repeat till you've cleared all that you want to remove.
"Live Long and Prosper but always carry a fully charged phaser, just in case!". Arrr'ow