Vice-Grips are not intended as machining clamps. Try the clamp bars in
the holdown kit, they are intended for the use and will give you high
clamping pressures when used properly.

BTW, have you been reading the Machining Fundamentals book? It explains
various work holding scenarios including the clamp bars.

I have been reading it, but not about clamps.

The majority of parts you make will have workholding issues. This is
probably the number one thing that separates a good CAM programmer
from a terrible one. You have to know how to make a part before you
automate it.

I'm big on optional stop in my program for clamp moves. Often a clamp
can be moved while the machine runs. If you got it moved before it
gets there, flip optional stop off and machine keeps going. if you
didn't finish, machine stops and waits for you.

Karl