Many hematological diseases are characterized by altered abundance and morphology of blood cells and their progenitors. Myelodysplastic syndromes (MDS), for example, are a type of blood cancer manifesting via a range of cytopenias and dysplastic changes of blood and bone marrow cells. While experts analyze cytomorphology to diagnose MDS, similar alterations can be observed in other conditions such as haematinic deficiency anemias, and definitive diagnosis requires complementary information such as blood counts, karyotype and molecular testing. However, recent works demonstrated that computational analysis of bone marrow slides predicts not only MDS or AML but also the presence of specific mutations. Here, we present and make available Haemorasis, a computational method that detects and characterizes white and red blood cells (WBC and RBC, respectively) in peripheral blood slides, and apply it to over 300 individuals with different conditions (SF3B1-mutant and SF3B1-wildtype MDS, megaloblastic anemia and iron deficiency anemia), where Haemorasis detects over half a million WBC and millions of RBC. We then show how these large sets of cell images can be used in diagnosis and prognosis, whilst identifying novel associations between computational morphotypes and disease. We find that hypolobulated neutrophils and large RBC are characteristic of SF3B1-mutant MDS, and, while prevalent in both iron deficiency and megaloblastic anemia, hyperlobulated neutrophils are larger in the latter. Finally, we externally validate these methods, showing they generalize to other centers and scanners.