Use Run->Remove workspace files from the Path Browser to remove files Perforce-managed files from your workspace. You can choose which files will be removed in the form that comes up; see Restricting Files Used in Commands for more information. The form also allows you to preview the file removal, showing you exactly which of your workspace files will be removed.
You can also remove single file from your workspace by running Run->Remove from workspace from the File Browser. This removes the current file immediately unless you have it open in your workspace.
Only your unopened files will be removed. Opened files must be submitted or reverted first before P4Web will remove them from your workspace.
If you use any other means of removing Perforce-managed files -- simply erasing them, for example -- the Perforce metadata about your workspace will be incorrect. To reconcile Perforce's metadata with the actual state of your workspace, you should use Run->Remove workspace files on files you've erased. To find out which files those are, use Path Browser's Show->Missing files command.
P4Web actually runs a sync command to synchronize to a special-purpose revision known as #none to remove files from your workspace.