Remember that density is one of the properties of a substance that can be used to identify it because it is an intensive property. An intensive property is one that does not depend on the amount of substance present while an extensive property does depend on the amount.
For density, we know that
density = mass/volume
If you cut the metal in half, you will reduce the mass by one-half but you will also reduce the volume by one-half so the ratio between the two will be the same. We can look at an example for aluminum
A 1-mL sample of aluminum has a mass of 2.70 g which gives a density of 2.7 g/mL.
If we cut the sample in half (i.e. 1.35 g), the volume of the sample would also be cut in half (i.e. 0.5 mL). When we do the calculations (1.35 g/0.5 mL), we still end up with a density of 2.7 g/mL).