Tunable X-ray sources from a laser-driven wakefield have wide applications. However, due to the difficulty of electron dynamics control, currently the tunability of laser wakefield-based X-ray sources is still difficult. By using three-dimensional particle-in-cell simulations, we propose a scheme to realize controllable electron dynamics and X-ray radiation. In the scheme, a long wavelength drive pulse excites a plasma wake and an off-axis laser pulse with a short wavelength co-propagates with the drive pulse and ionizes the K-shell electrons of the background high-Z gas. The electrons can be injected in the wakefield with controllable transverse positions and residual momenta. These injected electrons experience controllable oscillations in the wake, leading to tunable radiations both in intensity and polarization.