Organ printing utilizes tissue spheroids or filaments as building blocks to fabricate three-dimensional (3D) functional tissues and organs based on a layer-by-layer manufacturing mechanism. These fabricated tissues and organs are envisioned as alternatives to replace the damaged human tissues and organs, which is emerging as a promising solution to solve the organ donor shortage problem being faced all over the world. Inkjetting, one of the key technologies in organ printing, has been widely developed because of its moderate fabrication cost, good process controllability, and scale-up potentials. There are several key steps towards inkjet-based organ printing: generation of droplets from bioink, fabrication of 3D cellular structures, and post-printing tissue fusion and maturation. The droplet formation process is the first step, affecting the overall feasibility of the envisioned organ printing technology. This paper focuses on the ligament flow of the droplet formation process during inkjet printing of bioink containing living cells and its corresponding effect on post-printing cell viability and cell distribution. It is found that (1) two types of ligament flow are observed: at 30 V (Type I), the ligament flow has two different directions at the locations near the nozzle orifice and the forming droplet; at 60 V (Type II), the ligament flow directions are the same at both locations; (2) compared to Type II, fewer cells are ejected into the primary droplets in Type I, because some cells move back into the nozzle driven by the ligament flow in the positive z direction; and (3) cell viability in both Type I and Type II is around 90% without a significant difference. The resulting knowledge will benefit precise control of printing dynamics during inkjet printing of viscoelastic bioink for 3D biofabrication applications.