Cellular shades, also known as honeycomb shades, are mounted similarly to Venetian blinds. Brackets found at each end of the top of the shade hold it in place. There may be one or more support brackets in between depending on the shade's width. Review the type of shade that will replace the cellular shade before removing it. You might be able to use the same mounting system for the new shade, which would save you the trouble of removing the brackets after removing the shade.
Disconnect the shade's bottom from any hold-down brackets by bending them away from the shade's bottom bar. Use a screwdriver to pry the brackets free if they are stiff.
Raise the shade until it hangs about 4 inches deep. This keeps the bulk of the shade out of the way of the brackets and will give you access to the front and back of the brackets' assembly.
Insert the screwdriver between the tab on the bottom of a bracket and the top rail of the shade and pry it away. This will release the rail.
Repeat the process for other brackets, but leave the center support bracket in place. If there are no support brackets, ask a helper to hold the rail to prevent it from falling.
Tilt the back of the rail down toward you. This should free the front of the rail from the catch on a bracket. The rail now should be free of the end brackets.
Lift the rail up and toward you to free it from a center support bracket.