Q.mimosa tree only flowers on 2 of the branches
My mimosa tree has about 10 branches but only flowers on 2 of them. Isn’t that a bit weird? Why is that happening.
There are multiple tree species called mimosa; I will assume you are referring to the beautiful Persian silk tree, Albizia julibrissin.
There is no easy answer, especially without photos of tree and site and knowing more about the growing conditions, soil and water management. How long you have noticed this condition, and are there any other signs of disorder such as foliage discoloration thinning and branch die-back?
There is a serious soil borne fungal disease possible, "mimosa wilt". But it would cause wilting and dieback as well as the flowering disorder.
Water management is a key, if one side of the tree gets more water than the other the side with water deficit will suffer.
Drip irrigation systems often distribute water unevenly in the root zone.
Silk trees should be deep watered infrequently and allowed to dry out in between. They require well drained soil.
Root damage, root rot, restrictions to root growth are other guesses. Nutrient deficiencies or excesses could be a reason, if you don't fertilize adequately or if you overfertilize.
https://www.gardeningknowhow.com/ornamental/trees/mimosa/growing-silk-trees.htm
