I think that the best way to describe a growth marketer might be one part user researcher, one part marketer, and one part designer. You have to have an incredible empathy for the user. You also have to understand what the real benefit of the product is, and how it serves the customer in the most efficient manner. And then, you have to be able to translate all of this into an experience, a design, that the end user sees. This should cause action or reaction of the sort you want.
Experience matters. Why? Because a growth marketer is not a specialist. You need a wide skill set and deep time inside of different channels to get to know how they work. These experiences breed success in partnerships, emotional translation, and communication - key skills to have. You need time to explore and learn. And you're likely going to have screwed up - a lot - while you're learning. And this is all good, because failure is a better teacher than success.
A growth marketer is not an A/B tester. A/B Testing is just a tool, a final step to verify or disprove the entire process that goes before it.
Comfort with discomfort is often cited as the key to growth. Startups thrive in this space, while large companies do everything they can to avoid it.
An inquisitive mindset is required.