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PedroPinto
Your laptop doesn't do anything clever, it's just not earthed. My suggestion of lifting the ground doesn't do anything unsafe, it just emulates what you're doing when you're plugging it directly into your laptop by not earthing that connection.
Ground hum occurs when you have a potential difference between the points at which your system is connected to the earth. If you have a single earthing point you will not have a ground hum because there's no ground loop - you can't have a potential difference when you have a single earth connection. If you're using shielded phono leads and these are plugged into your MiniDSP then there will be a route to ground to whatever it is they're grounding to on the other end. Lifting the ground on a wall plug which is only connected to your MiniDSP will not be unsafe because it's exactly the same as plugging it into your laptop.