July Favre,
"Real cutoff" takes a large machine, heavy tools and toolposts, lots of power, speed and continuous coolant.
What kind of cutoff tool is it you are using? A simple high speed steel blade?
What are you cutting off: material and diameter of material? What style of toolpost?
You must cut very close to the chuck. If you are using a 3 jaw chuck to hold small diameter stock, the grip of the chuck is poor. Use a 4 jaw chuck, or better yet, get a collet chuck to grip round stock. You can even purchase a small collet chuck which you can hold in the main chuck for some types of work.
Do not part off between chuck and tail center: an obvious binding condition will arise near the end of the cut off and bend or break something.
Use coolant on the cutoff blade.
A bit of positive top rake (its actually called back rake, but its the angle of the top plane of the blade relative to the centerline of the lathe) on the blade will help. Most HSS cutoff blades are useless for anything except cutting off brass or cast iron, where zero top rake is correct.
A friend of mine used to use old 1" power hacksaw blades for cutoff on his small lathe. He would grind a real hook shape on the top of the blade, just behind the tip. With a real light feedrate, this will not clog up (too often). For light duty machines, this is often the approach that will work.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)