One simple solution for just about any saw hand fed, bandsaws in particular, is a Vee block. Stop off material before approaching blade, so there is clearance for the cut part to drop. The Vee block, or any spacer lets gravity create clearance as the part looses supporting mass and begins to droop.
When a vise is involved, conditions change........ a] contact with part (stop) shouldn't deflect from setting the part into position, b] the stop should have a radius, bevel or a secondary spacer so part is not bound between clamped part, rigid stop and moving blade.
The only sawing that operates dependably with both material and part clamped, are typical cold saws, having a vise on each side of blade. Heat generated by chop saws wouldn't like this rigidity. Many horizontal bandsaws have a retractable stop to alleviate binding due to the wide blades they use. Simple flat cams, and spring loaded bolt action rifle-like acting stops are the most common.
Quality of a vertical bandsaw cut is entirely a result of proper, or not proper conditions. A practiced craftsperson can cut a profile to 1/64" of layout.