Why is cladius so slow in punishing hamlet for polonius death?

He was not actually. After Claudius finds out, he sends Hamlet to England with Rosencratz and Guildenstern and with him a letter which would command the English king to kill him. He did not want to do it himself because Hamlet is popular with the people and he did not want to upset Gertrude, so it has to be done discreetly.