How does a ps2 mouse send data to a computer?
For a USB mouse, the data transfer is very complicated. First of all the host (computer) must discover the presence of the mouse (it may have been hot-plugged). Then, the host must find a device driver, and in the case of a mouse, this will be a HID (Human Interface Device) generic driver. Finally, the host will open USB endpoints and actually transfer mouse motion data in the form of X,Y co-ordinates and button up/down bits.

This is something that's hard to do with an Arduino. You'd need to get a USB host interface shield, and then write a sketch (program) to drive it. If you really want to interface a mouse with an Arduino, you may find it easier to get a PS/2 mouse (an obsolete PC-compatible standard) or a serial mouse (another obsolete standard, seen on all types of computers), or a quadrature mouse (very raw interface going directly to button switches and motion sensors).