process by which body produces blood cells?

Erythropoesis.

Answer: Bone marrow It is called Erythropoiesis; the process by which red blood cells (erythrocytes) are produced. Human: In human adults, this usually occurs within the bone marrow. Humans with certain diseases and in some animals, erythropoeiesis also occurs outside the bone marrow, within the spleen (Malay: limpa) or liver. The tibia and femur cease to be important sites of hematopoiesis by about age 25; the vertebrae, sternum, pelvis and ribs, and cranium bones continue to produce red blood cells throughout life. Fetus: In the early fetus, erythropoiesis takes place in the mesodermal cells of the yolk sac. By the third or fourth month, erythropoiesis moves to the spleen and liver.

In the bone marrow you have stem cells called Hemapoetic stem cells that are the precursors to all blood cells, red and white among other cells.