So, there are a number of devices in your consumer unit.
MCBs: Each circuit has an MCB - Miniature Circuit Breaker. This has a curve type (A, B, C etc, usually B Curve for home) and an Amp rating (e.g. rings on 32A, etc). It will trip out if too much current passes through the live.
RCD: Commonly twice the width of the above, has a test button on it, and measures the balance in the live vs the neutral. A difference over the rated allowance (usually 30mA) between live and neutral, and it trips. Has a test button on it. Effectively, this device is looking for the same current going out of live to be coming back in via neutral. If some current is going elsewhere (down the earth, through your leg, whatever) it trips. These usually cover multiple MCBs, and, crucially, any leakage will cause them to trip. So for example, you might think "it must be the garage, because even when all the other MCBs are off it still trips" but even if you've turned an MCB off, that's only isolated the live for that circuit. So some device with a short between neutral and earth that is currently completely unpowered on a circuit that is off, could still cause the RCD to trip.
RCBO: RCBOs combine the functions of an RCD with an MCB, and are the width of an MCB. They are newer and more expensive (£30 each rather than £3-4 each) but by having an RCD for each circuit, a fault only takes out that circuit and doesn't leave you sat in the dark.
Personally I like to have RCBOs on everything, it makes things much easier.
In any case, as long as the live and neutral are intact, what you have or have not done to the earth is irrelevant and won't trip the RCD. The RCD will only trip if there is a difference of current going out the live vs coming back in the neutral. Nicking the SWA cable and exposing the armour (which should be earthed, but isn't in your image, although might be at the other end) CANNOT have caused the RCD to trip, unless you hit it so badly that you went through the armour.