You sure can!
Head to https://ifttt.com/p/username/applets/private, click on the Applet you'd like to delete and click Delete to permanently remove the Applet from your IFTTT account. Please note, you'll need to use a web browser, deleting Applet is not currently available on the IFTTT app.
If you'd like to delete an archived Applet, you'll need to temporarily Restore the Applet before being able to delete it.
Note that Published Applets cannot be deleted because other users may be relying on them.