Controlling drop dynamics on solid surfaces is an important challenge. In many strategies for efficient drop deposition, drop dynamics is generally assumed to be axisymmetrical. We demonstrate shape-dependent impact dynamics that can considerably modify the dynamics by deforming the drop into a truncated spherical shape at the impact moment. Experimental and numerical studies show the exceptional rim dynamics that lead to reduced bounce heights compared with spherical drops. We investigate the impact dynamics of truncated spherical drops as a function of the truncation depth, surface wettability, and impact velocity numerically. The bounce height of the truncated drop reduces by 56% below spherical drops. To elucidate the mechanism for the reduction in the bounce height, we conduct the horizontal and vertical momentum analyses of truncated drops. The truncated drop impact can potentially open up new opportunities for enhancing drop deposition in practical applications, such as surface coating and spray cooling.