Hemoglobin is a protein that can be found in our red blood cells. It's job is to allow the red blood cells to carry oxygen to each of the cells in our body. This is critical to the cells as oxygen is needed to perform cellular respiration (the process that breaks down food molecules to release energy). The red blood cells also carry away the carbon dioxide that is formed as a byproduct of cellular respiration. All of this is made possible by the hemoglobin containing red blood cells. Without them, our cells would die. So, a mutation in the hemoglobin could, and would, easily affect each of the organ systems causing the organs to simply die due to the lack of oxygen and overabundance of carbon dioxide building up within the cells. In turn, this would lead the death of the organism.
Hemoglobin is made of three components: hemo, alpha (or alpha-like) globin, and beta (or beta-like) globin.
Changes in globin production (more or less than normal) can cause mutations in alpha or beta globin gene, these changes leading to one type of thalassemia, which is a quantitative hemoglobin disease.
Another blood disorder, caused by a mutation in the HBB gene is sickle cell anemia, where the cells have the C-shape. Cells' flexibility is reduced by the process of sickling and the risk of developing complications is growing. This kind of blood disorder could be found in regions where malaria occurs. In C-shape cells malaria parasite could be destroyed before emerging the daughter parasite.