I am unaware of any feature that currently allows us to get our segment definitions in JSON... I have actually talked to some people at Adobe about that.. allowing us to export and import segment definitions in JSON format (since I believe they are saved in the format)... whether or not that happens is unknown, but it would certainly make it easier to share and diagnose segment issues with other people (like here in the forums) so much easier.....
You could try the audiences API as was suggested... but not all segments are "audiences" and I don't know if that would return what you need or not...
You could try the Segments API, since there are retrieve and update endpoints?
https://developer.adobe.com/analytics-apis/docs/2.0/guides/endpoints/segments/