I am approaching this from the personality traits daya and krupa as emphasised in Hindu culture. I understand that "mercy" or krupa is a more sublime trait, as opposed to daya which is more everyday and ordinary.
I would say that mercy implies a justice system, whereas pity implies an external source of anguish to the suffering individual. So, mercy is when justice can be exercised but is restrained. Pity is when we witness suffering but do not have authority or power to reduce the consequence because the suffering is not the consequence of the suffer's actions. Pity would be given to the victim of an "act of God" while mercy would be given to a criminal. Just my thoughts.
Pity is external, you can pity someone and even give him/her some money but mercy is different. Mercy is internal. You do not need to experience everything in life. There is no single person that can experience everything in life but don’t ignore the pain of people who are going through stuff. For instance if a lady said to you how she had to go without food for days. She had to go back to breast-feeding her already weaned child so the child won’t die. You won't have to go without food before being merciful to her.