No, you have it backwards. Growth hacking is not a part of SEO. Rather, SEO is one of the tactics that can be used as part of growth hacking.
"Growth hacking" is a trendy term that essentially means "low cost marketing." In a nutshell, "growth hackers" do things such as analyzing their site metrics and employing A/B testing to figure out what works best, implementing SEO tactics to improve their reach via organic search and using social media and/or direct outreach to bring their business and product/service offerings to the attention of the buying public and the press.
Because they either don't have the budget or don't want to spend the money, they generally avoid paid advertising (such as print ads, broadcast, or pay-per-click) and other high priced methods of promotion.
Bottom line, it's a trendy phrase used to describe what smart small businesses and startups have been doing all along.
You may find this Wikipedia article helpful. https://en.wikipedia.org/wiki/Growth_hacking