How agnostics approach to life after death, and the living purpose of humankind?
How can you approach something that you don't believe exists?
By using the expression “living purpose of humankind” you by implication suggest a divine plan. Do you mean you think there is something after living that has a purpose? We who don’t believe in a creator don’t accept that there is another life after death.
Most agnostics and atheists, myself included, do not believe life after death exists or can exist - there is no post death consciousness, nor awareness nor being at all, the dead person has simply stopped. Others, including some on this site, have their own theories - some believe in reincarnation, some believe that the soul exists and continues to do after the body dies.
Living purpose is whatever you choose it to be. It can be to become as rich as possible, to be famous, to make others bow before you, to help others live happier lives, to create beauty, to increase knowledge... anything you want.
Most of us choose as our purpose to do as much good and as little harm as we can to our selves, our loved ones, our friends, other people, other lifeforms, and the environment. As far as life after death goes, we agnostics are still waiting to hear back from Harry Houdini.