We introduce SpreadPy as a Python library for simulating spreading activation in cognitive single-layer and multiplex networks. Our tool is designed to perform numerical simulations testing structure-function relationships in cognitive processes. By comparing simulation results with grounded theories in knowledge modelling, SpreadPy enables systematic investigations of how activation dynamics reflect cognitive, psychological and clinical phenomena. We demonstrate the library's utility through three case studies: (1) Spreading activation on associative knowledge networks distinguishes students with high versus low math anxiety, revealing anxiety-related structural differences in conceptual organization; (2) Simulations of a creativity task show that activation trajectories vary with task difficulty, exposing how cognitive load modulates lexical access; (3) In individuals with aphasia, simulated activation patterns on lexical networks correlate with empirical error types (semantic vs. phonological) during picture-naming tasks, linking network structure to clinical impairments. SpreadPy's flexible framework allows researchers to model these processes using empirically derived or theoretical networks, providing mechanistic insights into individual differences and cognitive impairments. The library is openly available, supporting reproducible research in psychology, neuroscience, and education research.