The low earth orbit (LEO) satellite-borne edge cloud (SEC) and machine learning (ML) based semantic communication (SemCom) are both enabling technologies for 6G systems facilitating computation offloading. Nevertheless, integrating SemCom into the SEC networks for user computation offloading introduces semantic coder updating requirements as well as additional semantic extraction costs. Offloading user computation in SEC networks via SemCom also results in new functional challenges considering, e.g., latency, energy, and privacy. In this paper, we present a novel SemCom-assisted SEC (SemCom-SEC) framework for computation offloading of resource-limited users. We then propose an adaptive pruning-split federated learning (PSFed) method for updating the semantic coder in SemCom-SEC. We further show that the proposed method guarantees training convergence speed and accuracy. This method also improves the privacy of the semantic coder while reducing training delay and energy consumption. In the case of trained semantic coders in service, for the users processing computational tasks, the main objective is to minimise the users’ delay and energy consumption, subject to sustaining users’ privacy and fairness amongst them. This problem is then formulated as an incomplete information mixed integer nonlinear programming (MINLP) problem. A new computational task processing scheduling (CTPS) mechanism is also proposed based on the Rubinstein bargaining game. Simulation results demonstrate the proposed PSFed and game theoretical CTPS mechanism outperforms the baseline solutions reducing delay and energy consumption while enhancing users’ privacy.