I built one along the same idea as the Lurecraft one, if that is prehistoric mine has to be somewhere around big bang time period then.
I cut ziillions of the things with out any problem. The one thing I haven't seen mentioned is salt content. If you are having tearing issues, my guess would be your plastic is too soft or you don't have enough salt. If you want super soft tubes, smallmouth is correct, injection is the only way to go. To get nice cuts, your plastic has to have some stiffness or the blades just smash it and tear like your talking about.
Try hardener or salt, let me know if that helps