As a state-of-the-art technology, micromixers are being used in various chemical and biological processes, including polymerization, extraction, crystallization, organic synthesis, biological screening, drug development, drug delivery, etc. The ability of a micromixer to perform efficient mixing while consuming little power is one of its basic needs. In this paper, a passive micromixer having vortex-generating mixing units is proposed which shows effective mixing with a small pressure drop. The micromixer works on the split and recombination (SAR) flow principle. In this study, four micromixers are designed with different arrangements of mixing units, and the effect of the placement of connecting channels is evaluated in terms of mixing index, pressure drop, and mixing performance. The channel width of 200 μm, height of 300 μm, and size of mixing units are maintained constant for all the micromixers throughout the evaluation process. The numerical simulation is performed for the Reynolds number (Re) range of 0.1–100 using Comsol Multiphysics software. By categorizing the flow patterns into three regimes based on the range of Re, the fluid flow throughout the length of the micromixer is visualized. The micromixer with dislocated connecting channels provides a satisfactory result with the mixing index of 0.96 and 0.94, and the pressure drop of 2.5 Pa and 7.8 kPa at Re = 0.1 and Re = 100 respectively. It also outperformed the other models in terms of the mixing performance. The proposed micromixer might very well be used in microfluidic devices for a variety of analytical procedures due to its straightforward construction and outstanding performance.