We develop simulation schemes for the new classes of non-Gaussian pure jump Lévy processes for stochastic volatility. We write the price and volatility processes as integrals against a vector Lévy process, which makes series approximation methods directly applicable. These methods entail simulation of the Lévy increments and formation of weighted sums of the increments; they do not require a closed-form expression for a tail mass function or specification of a copula function. We also present a new, and apparently quite flexible, bivariate mixture-of-gammas model for the driving Lévy process. Within this setup, it is quite straightforward to generate simulations from a Lévy-driven continuous-time autoregressive moving average stochastic volatility model augmented by a pure-jump price component. Simulations reveal the wide range of different types of financial price processes that can be generated in this manner, including processes with persistent stochastic volatility, dynamic leverage, and jumps.