This is actually a math question that starts out easy then goes to crap. The 120/70 tire's height is 70% of 120, or 84mm. The 120/60 tire is 60% of 120 or 72mm. That means the axle is 12mm lower to the ground with the 120/60 tire. But that also changes the rake or angle of the forks, and the trail. Plus, it also brings in algebra and I'm not going there.
But to save a few bucks, you have altered the height of the triple clamps, the rake, and the trail of your bike. Something that engineers have spent tons of time, calculations, and tests to get a good handling bike. Do you want to change that?