Reporting a paper cut is just like reporting a normal bug, which is explained here.

Once you've reported the bug according to those guidelines, there are a few more steps to follow to upgrade it to a paper cut.

Add a task for the One Hundred Paper Cuts project by clicking on the "Also affects project" link at the bottom of the list of affected projects, marked here in red:

The dialog you see will depend on whether or not this bug has already been reported upstream. If it has, then you can skip to the next step. If it hasn't, you will see the following dialog.

This dialog assumes you want to report the bug upstream, but that is not what we're trying to do here. Indeed, the bug should go upstream, but that is outside the scope of this question. Click on the link marked in red to "Choose another project". When you do that, you will see the following dialog:

Enter hundredpapercuts as the affected project and click Continue , and you will see the following:

The bug is now reported as a paper cut.