Hi HUxy,
We use "split up" to indicate break up or separate from a relationship. The preposition "from" is used to indicate separation, removal or exclusion. That is why the sentence is "split up from that.....".
Example: I split up from my wife after a five-year marriage. or We split up after a five-year marriage.
We can also write: I separated from my wife after a five-year marriage.
We can also say "I split up with my wife after a five-year marriage. The preposition "with" is used to indicate the relationship involved. So you are emphasising on the person involved in the relationship (my wife).
Hope this helps.
Cheers,
Lance