To create the illusion of making something invisible using mirrors, you first must make the mirrors invisible or the illusion is lost. This requires planning. An example is the appearing and disappearing head in a box sitting on a table. For the illusion to be effective, the walls, ceiling and floor surrounding the table must be a bland, uniform colour and the table positioned so two mirrors in a "V" shape are positioned between the three front legs of the table and aligned at a 45 degree angle to the walls.
Position the table so that three legs of the table are visible to the audience. From the view of the audience it will appear the fourth leg is hidden by the front table leg. Attach a mirror of the exact width between the square table legs and from the floor to the bottom of the table. Make the mirrors invisible themselves, with no seams visible and cleaned to perfection. Have an assistant position herself under the table behind the mirrors.
Carry an ornate wooden box of some type, showing it to the audience to prove it is empty and solid. The trap door should be sufficiently undetectable that members of the audience can handle it without detecting a false bottom.
Place the box, trap door side-down, with the hinged door facing the audience. Be careful not to walk between the wall and the table where the image is being reflected or your legs will be reflected, too. Talk to the audience as the assistant pokes her head through the trap doors in the table and box. Tap the top of the box and open it to show the head of the assistant now in the box.
Converse with the head and make a show of things. Then close the box, tap it, wave a wand, say the made-up magic words as the assistant slides his head back under the table and closes the trap door.
Open the hinged front door to show the head has disappeared.
Boxes for such tricks are available at magic shops. Get as much advice as possible before you perform this in front of a live audience, usually from the magic shop owner. Illusionists are an extremely tight-lipped group. Practice, practice, practice until you're satisfied.