Multi-scale dynamical systems are useful in modelling many systems with stochastic behaviour. The areas of applications range from climate science, neuroscience, biochemical reactions, evolutionary ecology, and mathematical finance. In this work we focus on models perturbed by symmetric alpha-stable noise due to their common appearance in modelling problems with heavy-tailed statistics. we consider models where the slow process converges to a deterministic one, and the fast component dictates the form of the noise in the rescaled deviations. We prove convergence of appropriately rescaled deviations from the averaged process, analogous to the type of diffusion asymptotics proved by Pardoux-Veretennikov in the Gaussian case. As in many earlier functional central limit theorems, we use the martingale approach to prove convergence of rescaled deviations and characterize the limiting process. This approach uses the solution to an auxiliary Poisson equation, based on the dynamics of the fast component with the slow component held frozen, and its regularity properties established from strong ergodicity of the fast component.