The entrained flow of an electrically conducting non-Newtonian, viscoelastic second grade fluid due to an axisymmetric stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equation into an ordinary differential equation. The issue of paucity of boundary conditions is addressed, and an effective numerical scheme has been adopted to solve the obtained differential equation even without augmenting the boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and skin friction coefficient. It is observed that in presence of slip, the velocity decreases with an increase in the magnetic parameter. That is, the Lorentz force which opposes the flow leads to enhanced deceleration of the flow. Moreover, it is interesting to find that as slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid.