Whenever I trim a stem plant, I cut the bottom few inches and roots off. If this is a nice, healthy piece, I replant it. Soon a new little stem and leaf will grow out of the cut area. Sometimes two separate ones have grown. Whenever this new top gets tall enough, I cut it off the bottom starter piece and have a new straight stem plant. You can usually tell where the old piece was and the new growth begins because the two sections aren't perfectly straight and in line with each other. Plants like Rotala will often grow multiple new tops and those get nice and bushy fast. Plants like Bacopa will get one or sometimes two tops.
Whenever I cut and replant a top, it just grows taller without any new side or top growth. If you want to start new stem plants, the best way is to replant that bottom part. Sometimes my Bacopa monnieri has started a new stem from the bottom of the mother plant (a new stem appears at the base of the plant coming up through the gravel) and when that's big enough I uproot the mother plant and cut the new stem off and replant it by itself.