When you place a crimson/warped sign on a wall and you break it with your axe, it won't be faster then when you break it with your fist. If you place the sign on the ground, it will be affected by the axe.
is duplicated by
MC-174725New Nether wall signs don't break faster with an axe
MC-170961Mining speeds for breaking crimson & warped doors, trapdoors, fences, signs, stairs and slabs aren't faster with an axe