You mean like this? Front lip circled in red.

I advise caution hacking lumps of metal off tools because it may be there for strength or to improve rigidity. But in this case, I think the lip is just to discourage coolant dripping off the front of the vice. Might be worth having if flood cooling is your thing, otherwise not. Off with it!
Should be fairly easy to remove. I'd clamp the vice upside down direct on to the milling table and mill it off. Otherwise a hacksaw and some sweaty hard labour would do it, approached from underneath Although Cast-iron is fairly soft once you get through the outer skin (already machined off the bottom), the lip might be chilled hard throughout. If so, bad luck! But persistence will get through it eventually. A cheap angle grinder fitted with any metal cutting wheel would do it easily – no need for diamonds.
Beware – cutting cast-iron is always horrid messy and angle grinders fling muck everywhere. Worth taking steps to contain cast-iron – lay sheets of paper, catch it in a box, good clean and change out of a boiler suit before leaving the workshop. Wear a hat – hair full of graphite is nearly as good as a paint brush. Above all don't stand in it and then walk across herself's snow-white carpet…
Dave