Any answer to this question would be pure speculation:
If it were that the entire chain is not made of seastone, any rational being would make the cuffs portion of the chains seastone and, therefore, he would not be able to cut the chains off without cutting seastone. This answer, though already accepted, could be rationally excluded.
Whether it makes sense that his devil fruit power could have been used to cut the chains is dependant on whether non-contact devil fruit abilities can manipulate seastone. I don't believe they can but the way to determine that is to look at smoker. Can smoker-san turn his entire jutte into smoke? If he can, then this is how the chains were removed. If he cannot, he must have done it by his own skill.
If a swordsman (combined with the strength of his sword/swords) is rated by what he is able to cut, Law may have been able to cut the chains by his own strength. His blade would touch the stones, not him. The seastone being as hard as diamond does not mean it cannot be broken; hardness is not the same as toughness. In other placed I would give better examples but for an anime site: the blades used in Attack on Titan are a super hard metal yet fracture/dull easily. Almost all very hard materials (especially stones and ceramics) have fracture planes between grain boundaries along which the material can be shattered or split with sufficient force. How did you think diamonds are cut? Why could Law do this and not Zoro? Law at that point in the story was a better swordsman by this rating criteria then Zoro was at the time when he considered cutting his hand (or his leg, or his chest, or throwing himself into a floating paw of pain... what is up with this guy?)
Finally please note that none of these explanations matter. One Piece is (and I love this) governed by the "rule of awesome" and the "rule of funny". What is possible and what the chains are made of is all what is fun for the audience. Both referenced scenes were badass and awesome. Why could Law cut the seastone and Zoro couldn't? Because it was a better show that way!