Not with one click but with just a few clicks: When you look at the list of comments, go to the last one and select it, then scroll up to the first one, hold down the shift key and select the first comment. This should select all comments. You can now delete them by right-clicking on one and selecting "Delete" from the menu. This should also work by selecting the first comment first, holding down the shift key and selecting the last comment, but I've had better luck with the process I described first.
You can also use the "PDF Optimizer" by saving the document as an optimized PDF (only possible in Acrobat Pro). Then from the different options you can select, make sure that only "Discard User Data>Discard all comments, form and multimedia" is selected (otherwise, more information may be removed from your document).