Legal Question in Intellectual Property in Illinois

That is copyright infringement.

Ditto. However, it is probably de minimis if only one copy is made and sold to only one person. No copyright owner is going to sue you over a single copy, but if you are mass producing copies (whether lots of copies of a single song or lots of single copies of different songs), you can expect to be caught and made to pay.

Cutting up the song will not likely avoid infringement as original parts are still original and thus covered by the same copyright. It is possible the CD producer did not register its copyright, and thus not entitled to statutory damages, but that would be highly unlikely.

Damages for deliberate copyright infringement can be huge. How huge can the damages be, you ask?

In the United States, statutory damages are set out in Title 17, Section 504 of the U.S. Code. The basic level of damages is between $750 and $30,000 per work, at the discretion of the court, but plaintiffs who can show willful infringement may be entitled to damages up to $150,000 per work.

Defendants who can show that they were "not aware and had no reason to believe" they were infringing copyright (that is, that they were not deliberately infringing) may have the damages reduced to $200 per work. However, if you made a 1000 copies that is $200,000.

So be smart and don't start.