No, there are clonal organisms.

> Would human reproduction to human societies be similar to mitosis to cells?

No; all the cells in a body divide on the terms the body sets and they die when the body does. (Or earlier, when so directed.) The only way for them to reproduce is indirectly, through the production of gametes. They do not and generally cannot have an independent existence. Human reproduction within human societies is the analogue of a cell within the body becoming cancerous. At that point, the cancer's uncontrolled mitosis is a form of independent reproduction, though it tends not to work out for the cancer because they almost never develop a way to leave the body, and end up killing themselves.

There are some exceptions, such as HeLa and the cancer that lives in Tasmanian devils.