Achieving precise control over a molecule's biological activity-encompassing targeted activation/inhibition, cooperative multi-target modulation, and off-target toxicity mitigation-remains a critical challenge in de novo drug design. However, existing generative methods primarily focus on producing molecules with a single desired activity, lacking integrated mechanisms for the simultaneous management of multiple intended and unintended molecular interactions. Here, we propose ActivityDiff, a generative approach based on the classifier-guidance technique of diffusion models. It leverages separately trained drug-target classifiers for both positive and negative guidance, enabling the model to enhance desired activities while minimizing harmful off-target effects. Experimental results show that ActivityDiff effectively handles essential drug design tasks, including single-/dual-target generation, fragment-constrained dual-target design, selective generation to enhance target specificity, and reduction of off-target effects. These results demonstrate the effectiveness of classifier-guided diffusion in balancing efficacy and safety in molecular design. Overall, our work introduces a novel paradigm for achieving integrated control over molecular activity, and provides ActivityDiff as a versatile and extensible framework.