If you need to cut a small piece of stock in the saw that can't be held because the moveable jaw is pivoting use a jack. In the attached pictures I needed to cut a piece of stock that would have been impossible to hold in the vise. I have some 1" dia bar stock that I centerdrilled and tapped 1/4-20 that I use as machinist jacks. (I made a couple 1" long and a couple 2" long.) I stacked them together and adjusted the bolt to match the width of the stock that I was cutting. This prevents the moveable jaw from pivoting and holds the stock tightly for sawing.
This trick also allows the movable jaw to be adjusted for a crooked face or odd shape on the stock. If you look carefully in the pictures; you can see that the movable jaw is slightly cocked to compensate for the non parallel faces of the stock.