If a stamen is removed from a flower as Mendel did in his experiments, will it grow back?

From that particular flower? Probably not. When the plant flowers again, the new flowers should have stamens.

"from a flower" No, it will not regrow. It's removal has no bearing on other flowers, only the one where the stamen is removed. Mendel took it from one flower and pollinated another flower. That is how hybrids are made.

There are other reason why you remove stamen from flowers. In Lilies removal of the stamen before pollen can be produced, I've seen and heard it can double the garden and vase life of the flower.

Also if you have noted a number of them in lilies if they drop on the carpet , place mats etc can stain , specially the orange / red and yellow ones so removal of them stops this. This is more so done when you have kids around as you know what their like.

The flower's purpose is to attract a pollinator, facilitate seed production and then fade away when the mission is accomplished. By plucking the stamens off lilies, you circumvent the floral foreplay so there's no pollen to trigger the process of reproduction.

So When the lily flower begins to open, simply pluck the pollen-less stamens from the flower. If you wait too long the pollen appears and resistance is futile.

Also yea they will not grow back once removed from the flower, though when other flowers grow they will have them.

Hope this helps