We study the structural and thermomechanical effects of cation substitution in the compositional family of metal-organic frameworks Zn_1-xCd_x(mIm)₂ (HmIm = 2-methylimidazole). We find complete miscibility for all compositions x, with evidence of inhomogeneous distributions of Cd and Zn that in turn affect framework aperture characteristics. Using variable-temperature X-ray powder diffraction measurements, we show that Cd substitution drives a threefold reduction in the magnitude of thermal expansion behaviour. We interpret this effect in terms of an increased density of negative thermal expansion modes in the more flexible Cd-rich frameworks.