When drilling stainless steel on a drillpress and clamping my workpiece on a machine vise the drill likes to grab the material right at the time when the exit hole reaches its final diameter. If I'm lucky, the bit will only slightly grab the material, without further problems. If I'm unlucky, the bit yanks the machine vise out of my hand, and smashes it against the table drills column or simply breaks, half of it stuck in the hole.
I usually use low cutting speeds (180-300rpm) and ample cutting fluids. A technique I use to reduce the problem is to drill the last 0.5mm at much higher speed (1000rpm) and very light downward pressure which works fine on flat, horizontal materials. If I'm drilling into round stock or something more complex, with internal holes I am forced to use my hand drill with torque control set to no more than 5nm. But this is hardly very professional.
Woodworkers put another sheet of wood below their workpiece to make exit holes nicer. With metal parts that's rather impossible, as the part needs to be clamped tightly in a vise. Is there a professional way of doing it without wrecking my tools?