Video object removal has achieved advanced performance due to the recent success of video generative models. However, when addressing the side effects of objects, \textit{e.g.,} their shadows and reflections, existing works struggle to eliminate these effects for the scarcity of paired video data as supervision. This paper presents \method, termed \textbf{R}emove \textbf{O}bjects with \textbf{S}ide \textbf{E}ffects, a framework that systematically studies the object's effects on environment, which can be categorized into five common cases: shadows, reflections, light, translucency and mirror. Given the challenges of curating paired videos exhibiting the aforementioned effects, we leverage a 3D rendering engine for synthetic data generation. We carefully construct a fully-automatic pipeline for data preparation, which simulates a large-scale paired dataset with diverse scenes, objects, shooting angles, and camera trajectories. ROSE is implemented as an video inpainting model built on diffusion transformer. To localize all object-correlated areas, the entire video is fed into the model for reference-based erasing. Moreover, additional supervision is introduced to explicitly predict the areas affected by side effects, which can be revealed through the differential mask between the paired videos. To fully investigate the model performance on various side effect removal, we presents a new benchmark, dubbed ROSE-Bench, incorporating both common scenarios and the five special side effects for comprehensive evaluation. Experimental results demonstrate that \method achieves superior performance compared to existing video object erasing models and generalizes well to real-world video scenarios.