We demonstrate strain-tuning of magnetocrystalline anisotropy over a range of more than one thousand Gauss in epitaxial Y3Fe5O12 films of excellent crystalline quality grown on lattice-mismatched Y3Al5O12 substrates. Ferromagnetic resonance (FMR) measurements reveal a linear dependence of both out-of-plane and in-plane uniaxial anisotropy on the strain-induced tetragonal distortion of Y3Fe5O12. Importantly, we find the spin mixing conductance G_r determined from inverse spin Hall effect and FMR linewidth broadening remains large: G_r = 3.33 x 10^14 Ohm^-1m^-2 in Pt/Y3Fe5O12/Y3Al5O12 heterostructures, quite comparable to the value found in Pt/Y3Fe5O12 grown on lattice-matched Gd3Ga5O12 substrates. ; Comment: 17 pages, 4 figures