In this paper, we examine the unsteady magneto hydrodynamic (MHD) flow generated by a disc that is making non-coaxial rotations with a third grade fluid at infinity and moving with a variable acceleration. The fluid is assumed to satisfy slip boundary condition on the disc. The governing equations are three dimensional and highly non-linear in nature. The assumed slip boundary condition is non-linear as well. The governing equations are transformed to a nonlinear boundary value problem which is solved numerically. Comparison of this generalized problem with uniformly accelerated disk satisfying no slip condition is made. Variations of the characterizing dimensionless parameters such as slip parameter λ, acceleration parameter c, unsteady parameter τ, third grade parameter β, suction parameter S, and magnetic parameter N on the flow field are discussed and analyzed graphically.