Try moving the gravel from around the base of the plant and pull the plant up slowly while wiggling slightly. If there is an extensive root system, trim the roots and leave some of it behind if it looks like you are going to make too much of a mess. You may have to trim some of the older leaves to balance the amount of foliage to the reduced root mass. if you are just separating the runners, pruning the tops shouldn't be necessary.
Once you are done, move the gravel back in place and vac the dirt that is on top. A small rigid tube with airline might work better to siphon the dirt without disturbing the gravel. Wave the tube aggressively over the gravel to stir up the loose dirt and siphon it off.
I'd shut the filter down while doing this so the dirt that does get pulled up doesn't get pushed all over the aquarium and cloud everything up. The dirt will settle faster in still water.