The solution depends on the ultimate goal... but let's say you can use "Route service with asynchronous execution", Then, there is a parameter "save_route_data" (Route service with asynchronous execution—ArcGIS REST API: Directions and Routing Services | ArcGIS for Developers). The generated zip file will contain File Geodatabase that will contain all route data. But let's say consuming File Geodatabase is not an option, then route result returned by server contains multiple record sets, such as route, stops, barriers, directions. So you need to convert every individual record set separately. Although, directions record set is not a regular record set and the conversion will fail so it will require some extra work to make conversion working.
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