Are there any good tools out there to help unbuilding a model, for example removing axles from beams?
Something like the famous brick separator, but for Technic models.
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Actually, the brick separator is a very versatile tool for disassembling Technic. The end of the wedge can be slipped into the slot on the side of several pieces to help pop Technic pins out from behind (I also use it like a screwdriver for aligning Technic pins while building). It can also be used to separate stubborn beam connections.
I've also got a 1:6 axle attached to the little axle pusher using an extender (sorry...I don't know the actual names of these things and I don't have time to look them up right now). It works great for pushing axles through deeper sockets, or for popping pins out from behind.
Other than that, I've never really had much trouble pulling Technic parts apart. I'm sure there are other uses I've yet to need, but that little orange tool has been a godsend for my sanity and fingertips. :)
I would recommend the 1:3 light grey cross-axle for popping other axles. It's more versatile than the 1:2 red cross-axle because it doesn't get stuck in the same spot you pushed whatever piece out of. It's also small enough that it's unlikely to bend or break under pressure, which is a necessity for this usage. (I'm not the only one who's bent a big axle on accident, right?)