Let's say you hand me a $100 bill, and that you have marked that bill. I then take that bill to a bank and ask for 3 $20 bills and 4 $10 bills. The bank takes that $100 and puts into the vault, and takes out the bills I asked for out of the vault. Later, someone comes in with $100 worth of bills, and asks for a $100 bill. The bank goes to the vault and gets the marked $100 and gives it to that customer.

Tracking the bill doesn't help, because as soon as it's in the bank, what happens to it (and how it's exchanged), is hidden from you. Mixers work the same way.