Mouse is a ubiquitous input tool crucial for user-computer interaction in modern society. However, the inherent trust in the mouse may pose security risks. If the mouse is maliciously manipulated, the connected computer could be secretly controlled, endangering personal privacy and property. In this paper, we introduce PuppetMouse, the first intentional electromagnetic interference (IEMI) injection-based attack that can effectively manipulate mouse clicks and movements without physical contact. By adjusting the parameters of IEMI signals, PuppetMouse can precisely control the click side, as well as the movement direction and speed. We demonstrate PuppetMouse's effectiveness on 14 wired and wireless mice from popular brands. The short response delay (within 4 ms) affirms the real-time performance of PuppetMouse. Robustness analysis across different attack distances and material occlusions validate the stability and reliability of PuppetMouse. Two case studies on firewall disabling and malicious WiFi connection further prove the severe threats of PuppetMouse in the real world. We also propose an integrated set of hardware and software-based defensive mechanisms to mitigate the risks posed by PuppetMouse.