HIV alone does not kill you.
When HIV progresses, it will begin killing the important cells in the immune system (these cells are called CD4 cells). Because of this, minor infections like the common cold become a serious health risk to the body as the immune system no longer has enough strength to fight off such infections.
HIV will soon progress into AIDS, which is an extremely serious disease that will completely take out the Immune cells in the body after short time. Individuals die from HIV/AIDS because of this, and not from the infectious diseases alone.