Semantic communication (SemCom) has emerged as a promising paradigm for 6G wireless systems by transmitting task-relevant information rather than raw bits, yet existing approaches remain vulnerable to dual sources of uncertainty: semantic misinterpretation arising from imperfect feature extraction and transmission-level perturbations from channel noise. Current deep learning based SemCom systems typically employ domain-specific architectures that lack robustness guarantees and fail to generalize across diverse noise conditions, adversarial attacks, and out-of-distribution data. In this paper, a novel and generalized semantic communication framework called WaSeCom is proposed to systematically address uncertainty and enhance robustness. In particular, Wasserstein distributionally robust optimization is employed to provide resilience against semantic misinterpretation and channel perturbations. A rigorous theoretical analysis is performed to establish the robust generalization guarantees of the proposed framework. Experimental results on image and text transmission demonstrate that WaSeCom achieves improved robustness under noise and adversarial perturbations. These results highlight its effectiveness in preserving semantic fidelity across varying wireless conditions.