Not in the USA for Coins, many places like Six Flags, Sea World have machines that will deface pennies to imprint their logo on them, it is only against the law if done to commit fraud,
See Title 18, Part 1, chapter 17, 331
Whoever fraudulently alters, defaces, mutilates, impairs, diminishes, falsifies, scales, or lightens any of the coins coined at the mints of the United States, or any foreign coins which are by law made current or are in actual use or circulation as money within the United States; or
Whoever fraudulently possesses, passes, utters, publishes, or sells, or attempts to pass, utter, publish, or sell, or brings into the United States, any such coin, knowing the same to be altered, defaced, mutilated, impaired, diminished, falsified, scaled, or lightened—
Shall be fined under this title or imprisoned not more than five years, or both.
Similar law for Debasement of Coins Title 18, Part 1, chapter17, 332
If any of the gold or silver coins struck or coined at any of the mints of the United States shall be debased, or made worse as to the proportion of fine gold or fine silver therein contained, or shall be of less weight or value than the same ought to be, pursuant to law, or if any of the scales or weights used at any of the mints or assay offices of the United States shall be defaced, altered, increased, or diminished through the fault or connivance of any officer or person employed at the said mints or assay offices, with a fraudulent intent; or if any such officer or person shall embezzle any of the metals at any time committed to his charge for the purpose of being coined, or any of the coins struck or coined at the said mints, or any medals, coins, or other moneys of said mints or assay offices at any time committed to his charge, or of which he may have assumed the charge, every such officer or person who commits any of the said offenses shall be fined under this title or imprisoned not more than ten years, or both.
Paper notes on the other hand appear to be illegal to render them "unfit to be reissued" Title 18, Part 1, chapter 17, 333
It appears the Feds are the only ones allowed to destroy Notes.
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.