General synonyms:
* Divide
* Split
* Branch
* Fork
* Separate
* Diverge
* Part
More specific synonyms:
* Dichotomize (to divide into two parts)
* Bisect (to divide into two equal parts)
* Cleavage (the act of dividing into two parts)
* Disseminate (to divide and spread out)
The best synonym will depend on the specific meaning you want to convey. For example, if you are talking about a road splitting into two, "fork" would be a good choice. If you are talking about a scientific theory being divided into two competing ideas, "dichotomize" might be more appropriate.