More then likey it will change due to a cut that is done with a blade or something that is dull. Even laser cutting is going to heat up the metal so it will change and possible bend or distort
Trivia: If you cut a block of iron in four pieces will the density change from when it was one piece?
Density is defined as mass per unit volume.
Read this and then answer your own question:
Of course not. Density is how much something weighs per cubic centimeter. Making it smaller will change the mass, not the density.
