Does it make more sense if we insert that?
to divide something into many small parts especially so that you can use the result for your own purposes
If not, then let us consider one of the definitions of so.
so
- in order that (often followed by that)
So we can reword the original into
to divide something into many small parts especially in order that you can use the result for your own purposes
Apparently you (OP) think that a comma would make sense "when spoken", but I personally didn't think it made a difference. This is because, typically, in the usual dictionary writing style, the word especially refers to the text the proceeds it, not precedes it.
I think there are a number of things that are strange with this entry. Two that I can formulate are
1. The entry goes from writing in the infinitive style (I don't know the correct name) to dropping the infinitive style and addressing the reader.
2. The entry drops the "that" in "so that".
Dictionary entries not usually address the reader. So that was odd. I also think "so that" sounds better, per se. Not because it is any more correct, but simply out of habit.
Maybe the learner dictionaries are different, or this particular entry is an odd, but I might have written it as
- to divide something into many small parts especially to use the result for one's own purposes
- to divide something into many small parts especially for one's own purposes