Yes, it is illegal to burn or deface currency in Australia. Defacing includes, cutting or drawing on.
The penalty is currently $5000 or 2 years in prison Australia wide.
Interestingly, even old coins like the 1 and 2 cent pieces are still protected by the same law, Section 16 of the Crimes (Currency) Act 1981 prohibits deliberate damage and destruction of Australian money without a relevant legal permit.
Burning money is illegal in;
- New South Wales
- Australian Capital Territory
- South Australia
- Western Australia
- Northern Territory