Record silence from the record, make a noise profile from it. Run noise reduction over the sample using said profile. It's best used in small amounts. If it's really bad, search for a MP3 or something online. If you can't find that, either oh well or settle into this being a beat with a noisy sample.
Oh, try cleaning the record too. That might help some. Getting rid of crackling and popping is pretty easy. I only know Audition but most editors should have that effect and it actually works really well and can be pushed hard and still yield good results. I like Audition because some pops are too big to be auto-cleaned but you can highlight the pop and there's an option for like remove big click and it'll get rid of it. If you don't have that option, i've always assumed that all it does is a split second limiter so maybe that might be an option.
