In article , Fred Splittgerber says...

Hi all,
I am aware of the fact that parting is (usually/always?) not recommended if
the workpiece is held between centers.
What about parting off with the workpiece mounted between a regular 3-jaw
chuck and a live center? (1/4 hp lathe, Workpiece: brass, 5/8'' diameter).

You can try but what will most likely happen is that
when you part through (or get close to going through) the
bit at the tailstock end no longer has any support and will
try to pivot out of the center in the tailstock. This
causes it to jam the cutoff blade and typically will snap
it.

Jim

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