What kind of cut-off tool are you using? There are high speed steel blades and carbide tipped (or insert) models.
The high speed steel blades pretty much suck for everything except cutting off brass and cast iron, where a neutral rake angle is called for. This is the angle that the top of the blade makes with the tangent to the work: 90 degrees.
This is not optimum for parting off aluminum or steel. Grind maybe 5 degrees top rake on the top of the tool (never grind the sides), so that there is a gentle slope that facilitates the chip sliding back over the face of the tool.
If you get a lot of chattering going on, this may indicate too much front clearance on the front of the tool. This should only be maybe 3 to 5 degrees, too.
The nicer avenue is carbide insert tools. These generally have a chip former pressed into the top of the insert. This helps wind the chip up like a clockspring, and also narrows it down a slight bit so that it comes out of the groove more easily.
Lube is very important, too. So is feedrate: a properly set tool likes to be fed in at about .003 to .004 per revolution. This is quite fast when you are hand cranking the tool. Slow down the feed as you approach the center for the final cutoff.
Carbide tooling is really the only way to cut steel. The spindle rpm is important for steel, too: the critical speed must be maintained in order for the tool to cut a smooth chip. Slower speeds leave a rough cut surface: when the speed is right, a nice shiny chip and surface result. But, in aluminum, you can seldom ever go fast enough to achieve this, so lube is the way to get what you want. Of course, constant surface speed on a cnc lathe is something you can dream about, too
