Other answers have covered what the micro inside the mouse needs a clock for. However they haven't covered the most important parts of the question:-
Wouldn't it be able to use the clock from the computer?
The first thing to note is that the computer isn't giving it a clock. If there isn't one to use, you can't use it. Unless you want to set up a custom connector, of course - but then you need to persuade all your potential customers to hand-modify their computers. Unless your customers are all extremely hardcore electronics experts, this isn't going to be a successful business strategy!
More importantly though is the question of why the computer isn't giving it a clock. In order for the clock to be fast enough to run the micro in the mouse, it needs to be pretty fast - a few hundred kHz is the absolute minimum, and more normally you're up into MHz for even very old micros. The 5717 apparently expected a 4MHz clock. The problem here is that unless you're very careful about the cable construction, signal sourcing and sinking, and all the associated interesting aspects of fast digital comms, what you create when you put 4MHz down a cable is a radio transmitter. It absolutely is possible to do this well without broadcasting to the world - USB, DVI and HDMI manage to send digital data at high rates - but it's by no means straightforward. So people generally don't send clocks down long cables unless they've got a good reason to do so.
Also if it has it's own crystal couldn't it get out of sync with the CPU clock?
You're absolutely right that if the mouse produces data which the CPU has to read clock-synchronously, then the mouse will need the CPU clock. (Actually you can get by with a slower synchronous clock and multiply up at the other end, but let's forget that for the moment, for simplicity.) So, does it?
Again, looking at the system, the answer is clearly "no". The 5717 changes its resistance as the user moves the mouse. The user isn't going to move the mouse that fast, and the user can move the mouse whenever they like, so there's no requirement for it to be clock-synchronous. Worst case, the resistance changes partway through the CPU reading it, and the CPU either gets the lower value or the higher value. The next time around, the resistance stays steady and the CPU gets the final value. Since the mouse is only moving at the speed of the user's hand, no-one much cares about one sample more or less to get to the final value.
So, to answer your questions in reverse order:
- It doesn't matter if it's out of sync with the CPU clock.
- There are good technical reasons for not sending the CPU clock down a wire unless it's absolutely necessary, and in this case it isn't so they haven't.