The objective of this article is to investigate the impacts of thermo-diffusion effect on unsteady axisymmetric Casson flow over a time-dependent radially stretching sheet with a multi-slip parameter and the force of chemical reaction. We employed an established similarity transformation to this non-linear partial differential system to convert it into a system of ordinary differential equations. The numerical results are attained for this system by using KELLER-BOX implicit finite difference scheme. It has great reliability and accuracy even a very short time period for computational simulation. The impacts of influential flow parameters on fluid flow are sketched through graphs and the numerical results are thoroughly argued. The temperature, velocity and wall concentration control parameters are analyzed. (i) It is witnessed that chemical reaction is not favorable to enhance the velocity profile. (ii) Multi-slip parameters vary inversely with velocity profile. (iii) The fluid concentration in its boundary layer decreases with the increase of heavier species, the parameter of the reaction rate and the exponent of power law for fluids having Prandtl number = 10.0, 15.0, 20.0 and 25.0. Moreover, the skin-friction-coefficient factor and Nusselt-number are compared with the published work. A strong numerical solution agreement is being observed.