The evidence shows it erupting repeatedly along that valley, but I don't there there's good evidence it actually "blew through" a mountain range. The eruptions have been following a path of least resistance but if the hotspot keeps traveling northwest like that it's actually going to end up underneath a mountain range and some geologists believe that will cap future eruptions for a long time.
It created a series of calderas through the state of Idaho. There were once mountains all along that diagonal path through Idaho (see diagram). A caldera is a huge volcanic crater.
They can also tell how large past eruptions were by the size of the ash and hardened lava deposits attributed to them.