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Analysis of an unsteady two-dimensional magnetohydrodynamic stagnation point flow of second-grade fluid is carried out in this article. It is supposed that the fluid is incompressible and impinges over the oscillatory stretching surface obliquely. The governing PDEs for second-grade fluid have been derived and then transfigured into a system of nonlinear coupled ODEs via appropriate similarity mappings. The BVP arrangement technique in Maple programming is used for the numerical arrangements of these subsequent nonlinear coupled equations. The outcomes are graphically represented and tabulated with the aim of illustrating the physical impacts of governing parameters on the temperature, concentration, and velocity profiles. The skin friction coefficient, Sherwood number, and Nusselt number are also analyzed by computational results, where it is reported that these physical quantities enhance with increment in Hartmann number and diminish with increment in the local second-grade parameter.