According to a number of clinical studies, coronary aspiration catheters are useful tools to remove a thrombus (blood clot) blocking a coronary artery. However, these thrombectomy devices may fail to remove the blood clot entirely. Few studies have been devoted to a systematic analysis of factors affecting clot aspiration. The geometric characteristics of the aspiration catheter, the physical properties of the thrombus, and the applied vacuum pressure are crucial parameters. In this study, the aspiration of a blood clot blocking a coronary bifurcation is computationally simulated. The clot is modeled as a highly viscous fluid, and a two-phase (blood and clot) problem is solved. The effects of geometric variations in the tip of the coronary catheter, including lateral hole size and location, are investigated considering different aspiration pressures and clot viscosities. A Bird-Carreau model is adopted for blood viscosity, while a power law model is used to describe the clot rheology. Computational results for blood clot aspiration show that the presence of holes in the lateral part of the tip of the catheter can be beneficial depending on clot viscosity, hole features, and applied aspiration pressure. In general, the holes are beneficial when the clot viscosity is low, while aspiration catheters without any extra lateral holes exhibit better performance for higher clot viscosity. However, when higher aspiration pressures are applied, the catheters tend to behave relatively similarly in removing clots with various viscosities, reducing the role of the clot viscosity.