Does the density of a mineral depend on the size of the mineral sample?

No, to tell how hard a mineral is you either have to test it or determine what mineral it is. Testing uses materials of known hardness such as a fingernail, or copper penny, or scratch plate, if the mineral is scratched by whatever you use to test it is softer. Hardness however is not based on size it will be the same for any sample of the same rock no matter what the size because its based on atomic arrangement and bond type.