Are there any chances of getting aids from getting aids blood on a cut?

Possible: Health-care workers have on rare occasions become infected with HIV by being stuck with needles containing hiv-infected blood. A few have also become infected by hiv-infected blood getting into the bloodstream through an open cut, or splashing onto a mucous membrane (e.g. The eyes or the inside of the nose). There have been only a very few documented instances of patients acquiring HIV by workers.

Yes.: Any time you have an open wound that is exposed to a patient with hiv/aids, there is a risk to becoming infected. The risk is very small, however, you should be checked out by your physician - they may want you to be tested and/or treated prophylactically depending on the circumstances.