How can I politely tell a professor that I'm too busy to do research with him this term?
Just say so directly! He will value your directness and honesty – 'beating around the bush' gets rather tiresome. There's enough of that from management...


  I'm sorry that I don't have time to work with you this term, as I have now started on a research project with Prof A that I am committed to finishing. However, I would still really like to work with you in the future. Since I aim to finish my current project in a few months, around the end of June, would you mind if I contact you again then?