my dear friend;
i guess that your sentence is a subjective clause which means two subjects it has.
it is created by two sentences:
1. she saw a mouse.
in this one SHE is your subject.
2. the mouse was going up the clock.
in this one THE MOUSE is your subject.
when they come together, we will have something like this:
She saw a mouse the mouse was going up the clock.
but this is completely false. We have two mouse here, so we omit the second one and we use relative pronouns like (( who, that, which and etc.))
the correct one is this:
She saw a mouse which was going up the clock.
I hope you have found it useful