A method of operating a cleaning system removes support material from parts made by a three-dimensional printer. The method operates the cleaning system to correlate data for features on a part located within a receptacle with structural data in a file used by the three-dimensional printer to fabricate the part. The method then operates one or more actuators to locate a fluid directing nozzle pneumatically connected to a pressurized fluid source opposite areas containing support material and operates the pressurized fluid source to enable pressurized fluid to be directed by the fluid directing nozzle at the support material. The method includes generating image data of the cleaned areas with an image sensor so the removal of the support material can be confirmed, and if an area is not sufficiently cleaned, the cleaning operation can be repeated.