The speaker is telling you to forget something.
He says "Forget i) that still unwritten report ii) the backlog of paperwork that is building up on your desk." With the "or", this means that these are simply two examples of the type of things that you should forget.
He then continues with the reason you should forget them (and he uses a comma instead of a semicolon - it's essentially a new sentence):
"On this cold and rainy mid-week night, there can be no excuses to stay late in the office".
There are no excuses to stay late.