A couple of thoughts,
You can make the cut manually. I do on all my 7800 prints as I don't want them to fall into the crappy basket. Once the print is done, use the feed buttons to bring the top of the print back up to where you can see it through the front cover. Then move it down about 1/4" to where it't out of sight. Turn the printer off, open the cover and let the two plastic holders make slight contact with the print. Now to the print head, and hit the release button, slide the head to the middle of the print, and hit the same button again but hold it down as it is also the cutter. Cut from the middle to the far left, release, and then come back to the middle and finish the cut from middle to right edge. The print won't fall since the two plastic holders have it.
You can replace the blade also if you feel it's dull. Epson sells replacements. The manual shows the method of replacement. However on thicker papers, I would consider making the cut yourself.
I don't think there is anyway to adjust the blade, i.e. make it cut deeper.
One other idea, is to install a device called a blade groove. I have one on my 9880 and love it. It fits on the very bottom of the paper guide and allows you to use a craft blade to cut your paper/canvas. I think their site is:
http://bladegrooves.com/Paul C