Is anemia caused by your spleen?

It depends. In some forms of anemia such as autoimmune hemolytic anemia, the spleen is actively involved in the pathophysiology of the disease. In other types, such as iron deficiency, the spleen has nothing to do with the disease.
Many causes. Anemia has a long list of causes including mineral deficiencies, co-morbid diseases, autoimmune disease, medical treatments can induce anemia, etc...