Great - identifying the problem puts you half-way home.
Just to make 100% certain, I’d probably connect a temporary jumper wire – just route it along the cable chain with a little tape here and there to keep it in place. Then run a test sequence to make sure everything works.
Once you are 110% positive it’s the wire…
The 1.03 (and earlier, I think) Mini’s used individual, generic AWG24 stranded wires in the harness. The 1.04 model switched to pre-made IGUS Chainflex cables, which look like multiple wires inside a larger sheath. Mini 1.03 and earlier also had a silver bed, whereas I think all the 1.04’s have a black bed. You likely have a 1.03 – as the IGUS Chainflex on 1.04 are way less prone to breaking.
If you have a 1.03… Just get some good quality, insulated AWG24 stranded wire (same color as the old to keep things organized). Work the wire through the plastic cable chain, and then into the black plastic “split loom” going to the control box. It’s tedious work, but doable. Once you get it all the way to the control box, you can cut the old wires ~1" from the terminal, then splice those ends (with the terminals) onto the new wire. (If you have terminals and a crimper, obviously that’s better – but if not, you can splice/solder/heatshrink the old terminals onto the new wire.)
If you have a 1.04… To do a “perfect” replacement, you’d need to identify which IGUS cable contains the bed ground wire – and then purchase that pre-made cable, with terminals. Same process, but larger multi-wire cable, more connections, and harder to get through the cable chain and split loom – I think you’d have to do some disassembly to go that route. Alternately, you could just add a new single generic AWG24 wire, just as described for 1.03. It won’t be “OEM”, but it will work.
If you have a 1.04 and decide to replace the IGUS cable… I recommend contacting Lulzbot support or itworks3d.com and see if you can get their help identifying the specific cable p/n that contains the bed ground wire, and just buy the cable from them.
For that matter, even if you go with an individual AWG24 wire, Lulzbot or itworks3d.com may be able to sell you a premade wire with new connectors. So I’d probably start by giving them a call – they can help identify what you need, and I’m sure one of them can help with the wires/terminals. They may even have some good tips for the replacement process.
Only other thought… If that wire has broken, you may have others near failure – as all the others have all undergone the same number of bends. The best guarantee for long, trouble-free service would be to replace all the wires in the harness, but obviously that’s a ton of work and may not be necessary. If everything else is working, I’d suggest just replacing that (1) wire for now.
*** All of the above assumes your printer is no longer under warranty, or don’t want to ship the printer to Lulzbot. Because if it is still under warranty, I’m pretty sure Lulzbot would happily fix the problem – although you’d likely have to pay shipping costs, which aren’t cheap. ***
Let us know how it goes!