Mercy is one of the three defining signs of Klal Yisrael as they are people who perform kindnesses, they are bashful and are merciful. Chazal already said that “Whoever has mercy on the creations of Hashem will receive mercy from heaven!”, as it says “And He will give you mercy and He will have mercy on you!”. A person must try and have the same attitude as his Creator about whom it says “And His mercies are over all things made by Him!”, and therefore one must have mercy on all living creatures. Hashem has so much mercy that he is even merciful to give time to those who have transgressed His will and do good to them even at that exact moment that they are making Him angry. In this and many other ways Hashem has unlimited mercy on His creations to a degree that is unfathomable by our intellect, and we must follow in His ways.
It is known that the prohibition against causing pain to living creatures is a biblical one and that one may not therefore hit dogs or cats who have caused damage especially as they did not do it to cause him harm and this is the way they get their food. All the more must we be merciful to human beings who have been created in the image of G-d and to our brothers of Klal Yisrael as we are all the sons of one man and like one man with one body. Even if a man has done bad to someone and done bad things to him he should not repay him with his bad way, nor should he take revenge or bear a grudge. Instead, he should have mercy on him and help him in any way possible and in the way that one treats others so is one treated.