Mortally describes something that happens in a way that causes death. If your guinea pig is mortally ill, it unfortunately means that he's certain to die.
You're most likely to come across the adverb mortally followed by the word "wounded." For example, a wildlife biologist might describe finding an injured owl that turned out to be mortally wounded, or hurt so badly that it later died. The key to this meaning is the word mortal at the heart of mortally — it means "doomed to die," from the Latin root mortalis, "subject to death, mortal, or human."