'to speak' is the default meaning of this verb, but you can still use it in 'to blow' sense when talking about wind.* Imo that's interesting because the same root is used in the word puhuri, which is a strong gust of wind.
*Not super common, but you hear it sometimes.
Puhkua is more like to huff or to puff: to breath heavily or to blow with strong puffs. "Normal" blowing is puhaltaa.
By the way...
löylyttää = to beat up someone, to rout someone
verilöyly = slaughter, massacre (lit. blood löyly)
At first I couldn't understand how it's possible to start with lovely sauna steams and end up with slaughter and beating, but then I remembered how I once went to a swimming hall sauna. It was almost empty, there was only one woman there. Quite soon after I had sat down, she asked me if she could throw more löyly. I didn't see the imminent danger I was in, so I answered 'sure!', and so she took the ladle and turned the sauna into a furnace. And I couldn't even leave because I had just assured her I wouldn't mind it!