The head-on collision of drops is governed by the interfacial tension, viscosity, and inertia of the impacting drops. Earlier studies show that depending on the relative magnitude of these forces, the outcome of a head-on collision of two identical drops of the same liquid is likely to culminate in coalescence or reflexive separation. In this study, the head-on collision of drops of miscible liquids having dissimilar viscosity has been investigated numerically. As the two drop liquids are miscible, it is anticipated that the average viscosity of the two liquids will replicate the transition boundaries of coalescence and reflexive separation for a single fluid. However, numerical simulations reveal that this is true only for low-viscosity ratios. A high-viscosity ratio creates asymmetric flow; hence, the average viscosity does not accurately represent the local viscous effect. The asymmetric flow also facilitates the pinch-off of a thread without the separation of a satellite. The present investigation reveals that viscosity contrast leads to two additional outcomes of the head-on collision of drops: encapsulation and crossing separation. We have built a phase diagram identifying the outcome of a head-on collision of dissimilar viscosity drops on the viscosity ratio (μr)-Weber number (We) plane based on the results of approximately 450 simulations.