The key words to understanding section 333 are "with intent to render such bank bill, draft, note, or other evidence of debt unfit to be reissued"

Most people will understand this as defacement (such as shredding) so as the bill is no longer able to be used as a bill (i.e. no one would take it). In reality, in means more along the line of defacement so as when the bank takes it as a deposit and realizes something is wrong (likes it's half a $20 and half a $2 taped together but counted as $20). Now the bank can't re-issue it.

Bottom line, it's not illegal to tear up your own money.

U.S. Code as of: 01/19/04
Section 333. Mutilation of national bank obligations

Whoever mutilates, cuts, defaces, disfigures, or perforates, or
unites or cements together, or does any other thing to any bank
bill, draft, note, or other evidence of debt issued by any national
banking association, or Federal Reserve bank, or the Federal
Reserve System, with intent to render such bank bill, draft, note,
or other evidence of debt unfit to be reissued, shall be fined
under this title or imprisoned not more than six months, or both.