The present paper interprets the unsteady magnetohydrodynamic (MHD) flow with heat and mass transfer over a stretching sheet embedded in a horizontal porous medium. The effects of viscous and Darcy dissipation, heat source, and chemical reaction is elaborately discussed in the presence of multiple slip effects for velocity, temperature, and concentration. Introducing a similarity transformation, the governing partial differential equations are transformed into a system of nonlinear, coupled partial differential equations. The asymptotic analytical solutions are obtained by using double-parameter transformation perturbation techniques and, compared with the numerical results and the verification of the computational code made with the earlier works, serves as the benchmark of reliability of the present study. The important findings reported herein are: porosity acts as an aiding force for the fluid velocity, more dissipative heat leads to higher velocity and temperature, chemical reaction parameter adversely affects the concentration. The main motivation behind this study is to perform the fluid flow, heat, and mass transfer analysis of a Newtonian fluid with mixed MHD flow, which has important applications in many industries, in particular, the process of extrusion/layer of fluid dispersed with solutal particles is extruded over other materials to increase the strength and durability of the final product.