My ex is living with her new boyfriend; can I stop paying spousal support?

Maybe.  

Experienced Bay Area Family Law attorneys will tell clients that In California, if a supported spouse is living with a non-marital partner, there is a rebuttable presumption that there is a decreased need for support under Fam C §4323(a).  What this means is that the burden of proof is on the supported spouse to show that, despite the cohabitation relationship, her need for support has not decreased. 

 
 In Marriage of Bower, the Court found that “[c]ohabitation may reduce the need for spousal support because ‘sharing a household gives rise to economies of scale. Also, more importantly, the cohabitant’s income may be available to the obligee spouse.'” 
To raise this issue with the Court you do not need to prove that that your ex has a boyfriend, but you must show that relationship has to be more than a roommate/boarder arrangement meaning that either there must be a sexual relationship or a homemaker-companion relationship. Marriage of Thweatt.  And while you may not be able to stop paying the entire amount of support, you could substantially decrease your monthly payments.