Do they still blow them up?

I was wondering about this too... According to the local news (as of last night) they didn't know how they were going to get rid of it yet.

Currently they are performing an autopsy though to try and figure out how it died.

I don't know that it was every common to blow them up. There's a news report from the '70s, widely watched on YouTube, of a whale carcass exploded by dynamite in Oregon. It didn't go well for them.

You can read more about the “Exploding whale” on Wikipedia, too https://en.wikipedia.org/wiki/Exploding_whale