It would be possible—although a bit awkward—to form the sentence without any commas at all:
My daughter so pure didn't know what I was speaking about.
This would only make sense if you had two or more daughters, and only one of them was so pure, so you're adding essential information in order to disambiguate the one daughter from the others.
Assuming you only had two daughters, one so pure and one so evil, it would contrast with the reverse:
My daughter so evil knew exactly what I was speaking about.
This can be compared to the following:
My brother, in San Francisco, is tall.
→ You have a single brother who lives in San Francisco.
My brother in San Francisco is tall.
→ You have more than one brother, and it's the one who lives in San Francisco who is tall.
The difference between the pair of commas and no commas at all is the difference between nonrestrictive information and restrictive information.
In no case can you have just a single comma as in your second sentence.
The only reason the my daughter so pure sounds a bit awkward is because we would normally use a pronoun in that situation.
Although it's not absolutely required, the restrictive version of the sentence would more likely be:
My daughter who is so pure didn't know what I was speaking about.
Note this version also has no commas at all. The reason that it doesn't sound as awkward with the commas is simply because of the pause they add as we read the sentence.