Relaying a signal to use satellites for navigation under a mountain makes no sense, since that way you only get the position of the relay you have set up, not the position of the main interest that it is linked to.
GPS also does not help you to determine your level precisely (="altitude").
They most likely have used extremely precise theodolites, or technical clones of these: instrumentations that developed the principle further for greater precision, but base on theodolites' basics. That is what I also take from the article Oberon has linked, as far as I understood it.
The woprk took ten years, but it was planned over decades. Also, they have had a referendum in Switzerland, where the people got asked whether to build it or not. A vast majority of the Swiss voted "Yes" back then.
There are plans and visions in Switzerland to tunnel even more traffic in the country, not only under mountains, but in flat areas as well - to get the traffic density disappearing from the surface. In parts of Swittzerland and Austria, truck traffic is a big problem, along the major axis of transit traffic from Northern to Southern Europe.
Hope the Swiss never find a Balrogh.
