Go shopping for:

Wood:

2.5' x 2.5' of 1/4" plywood

2' of 2" x 2" wood beam

1/3' of 1" thick wood dowel

Metal:

4' of 1/4" thick metal rod

1' of 1" diameter  1/8" thick metal tube (hollow)

Fasteners etc:

Hockey tape

Fishing line

4 x 1/4" nuts, bolts and washers

2 x 1" pipe clamps

Wood  glue

Off-the-shelf:

Nail clippers x 2

Magnifying mirror of your choice

Cut four 1' x 1' peices out of the plywood, probably use a table saw.

 (Clamp the two sides together to do both at once for the next few instructions)

Cut 45 degree angles at 3.5" the edge on two of the wood squares.

Drill a 1/4" hole on the each side face at about the height and depth of where the angle cut begins/ends.

Drill two more holes per side face of wood that are 4" from the first holes. The first hole is directly above the lower hole, the second is 45 degrees forward.

This step is up to you and your mirror that you bought. It probably has a metal rod that you can use to attach to your base. Drill a hole that fits the rot and lets you position the mirror how you would like.

Use a hand jigsaw to cut a slot from the two upper  holes on the side faces. This lets your nail clipper holder rotate about the lower hole and lets you position how forward or backward the clippers are.

Use a drill to put holes 1/2" inwards from the corners of the top piece. Use a jigsaw to connect the bottom and top hole on each side. Then, use the jigsaw to cut a rectangle that is 2.5" wide towards the middle of the top piece. This gives space for the nail clippers to fit into when they're lowered to the box.

Cut the wood beam in half.

Cut the metal rod in half. 

Drill a 1/4" hole 0.5" from the end on both, and then 4" from the first hole. These holes should align with the holes you drilled on you wood base sides.

Cut the tubes in half. Drill 1/2" hole about 1" from the end that just fits the thickness of the metal rod. Use a rotatory cutter or mill to cut a slot (about 1/8") down the length of the tubes. This lets the tube close on itself as it's clamped. To hold the nail clippers.