If you are offshore, you can re-apply for another visa, you may be asked to give a reason for the previous cancellation or refusal.
On the contrary, if your visa is refused or cancelled while you are onshore, Section 48 of the migration act 1958 restricts the applicant from applying for any substantive visa. However, there are options to counter this problem and a registered agent can provide you with lawful assistance in circumventing this issue.
Visa application can be refused or considered invalid if it is not applied correctly at place, on correct forms, correct class or if not correctly paid a visa, case officer will refuse to grant or accept this application.