An abrasive supply system may, for example, be used to supply abrasive particles such as garnet to a cutting nozzle of an abrasive jet cutter. According to an embodiment, the abrasive is propelled by a substantially constant flow rate gas source. According to an embodiment, the system may be supplied with abrasive from an atmospheric pressure abrasive hopper. According to an embodiment, a controller automatically actuates refilling of an abrasive tank from the abrasive hopper, and then automatically closes an abrasive supply valve and restarts abrasive propulsion. According to an embodiment, the controller may include or consist of pneumatic logic.