Depending design of a particular desk, a removable hutch is likely secured to the top using fastening hardware. By removing this hardware, you can lift the unwanted cabinetry from the desk top. If the hutch is structurally connected to the desk, you might have to employ a saw to remove the hutch in order to create a flush surface.
Secretary desks vary in the type of fasteners used in their construction. It is important to identify the key elements of the design before disassembling the desk.
Remove any loose material or shelving from the hutch before removing any hardware. Using a secondary support system on the hutch prevents injury as removing the joining hardware could cause the hutch to wobble or fall.
If the hutch was assembled separately from the main desk, it is most likely fastened by screws to the desk beneath it. These screws are visible from the exterior of the desk or are hidden in a pocket hole, a technique used to hide the obvious evidence of a screw head. Flat-pack furniture often uses a cam lock and nut fastening system wherein a small, round cam lock is removed before the corresponding screw can be unscrewed.
You may need to sand the surfaces where the adhesive was used to secure the hutch to the desk.