For some types of fruit trees, leaving a leaf or several leaves cut in half can be beneficial but for Mangos, it is not necessary.
Even preparing the scion by clipping off the leaves in advance is not necessary as long as you have a good apical bud that is swollen or the scion has swollen buds on it somewhere but prepping the scion will give that much more advantage.
When you graft a tree, there are lots of tricks you can do to increase the odds of a success. If a scaffold branch or secondary branching has three other smaller branches coming off it, you can graft all three branches if you are not limited on the availability of scions.
By doing all three branches at one time, you are removing a lot of apical dominance growth inhibiting hormones that suppress growth. If you only grafted one of the three branches, some of the energy going to that branch can be distributed to the remaining two branches that weren’t grafted. When you graft all three at once, the energy will be distributed to all three grafted scions so you have a good chance of a take.
If you are limited on scions, you can trim off nearby branches to redirect energy towards your grafted branch. In all these cases, you have to remove buds and branches that want to emerge after you remove the apical branch for grafting.
In some cases, you will need to leave some growth behind to keep the branch active but assuming you have an established tree with lots of branches and leaves, you may not need to do this.
Simon