According to the manufacturers the glyphosate products must be taken in by the target plants leaves to work. Some people swear that cutting large plants down and painting the stuff on the stump is just as effective, no matter what the makers of the products say, even though the vast majority of what is there in the stump is dead tissue.
How to apply any product is usually listed on the label and that should be followed. The safety of any product is another matter altogether.

I didn't mean cutting it back to the stump. I meant cutting back some of the foliage, so there isn't as much foliage.For instance if a bush is 3 feet tall cutting back to 1 foot because the full size will require a whole lot of Round Up.

You need to get the glyphosate into the plant, which occurs best through the foliage. If you cut 2/3 of the plant away, you will still have 100% of the root system to kill with 1/3 or less of the leaf area available to absorb the herbicide. Makes it much harder to kill the plant.

Gotcha

I have seen official website suggesting using the product on the stump (see attached link on Brazilian Pepper/An invasive tree in Florida). It may very well be that the manufacturer simply want you to use a greater quantity. Personally, I would try first on the stump using the minimum amount of Round-Up.
Best

Here is a link that might be useful: Brazilian Pepper Tree Control

Hackberry seedlings come up by the zillions in my yard. I keep a small spray bottle with full strength broad leaf weed killer in my pocket and when there is one I can't pull up I cut it off, put a drop of weed killer on the cut and that takes care of it.

This works when they get large as well, large enough that I have to use the loppers on them. They especially like to grow up inside of my mother's antique roses where it would be impractical to try to spray the leaves without getting it on the roses so I lop the hackberry as close to the ground as I can and drop on the weed killer. They seldom grow back. If a drop happens to get on a rose leaf I simply pull off that leaf. Roundup may do the same thing, but I happen to use the broad leaf killer.