We intend to travel from Innsbruck (Austria) to Munich (Germany) via Mittenwald which is reputed as a scenic train route between the two countries. Please advise the cheapest way to do this.
surely ride from Innsbruck to Munich via Mittenwald train is more scenic rather than straight train from Innsbruck to Munich. i have used this route couple of times and found cheaper. First train ticket from db train website Innsbruck to garnish Partenkirchen would cost around 12 to 14 euros. Second journey from garmisch to munich through bus from flixbus website and ticket would cost somewhere between 5 to 8 euros , also if booked in advance bus ticket might be lot cheaper.
On the German side, i.e. from Mittenwald northwards, the cheapest ticket is the Regio-Ticket Werdenfels, hands down. It is €19 for a single person and an additional €4 for every further traveller. It is now valid for an entire day for unlimited travel in DB’s Werdenfels network and the Munich S-trains. All the lines are highlighted on this map. Note that you must use regional trains (RE and RB; the red ones) and cannot use ICE trains. But that is okay, since regional trains go every hour and there are only a few ICE trains on weekends last time I checked (and the Innsbruck–Mittenwald leg seems to have been discontinued).
On the Austrian side, I am not aware of any special offer tickets. The single fare is €10.60 for a flexible ticket or €10.20 if you choose your train in advance.
The route is most definitely scenic; you can check out a few pictures on this site.