Glad to see someone wanting to get into clay target shooting - its a lot of fun. A pump is handicap on clay games with pairs, but that can be addressed down the road.
There are only two games that do not allow a pre-mounted gun - International Skeet and FITASC - the international version of sporting clays. I mention that because you say you have no issues with the gun premounted. Unless you are shooting one of those disciplines, start with the gun mounted and work on the particular aspects of the game you are doing - foot placement, follow through, swing dynamics, lead, target acquisition, etc.
It MIGHT be something as simple as a poorly fitted stock, it might not - without a knowledgeable person actually watching you, it is difficult to say. Perhaps your local gun club has someone who can watch you and determine the cause.
Good luck and welcome to the FUN side of shotguns