Cast iron drain pipe replacement
You should use plastic (ABS) for any replacement runs if possible. Yes you can use clamp couplings underground (for iron-to-iron and iron-to-plastic connections) but not just any type. You need heavy duty clamps listed for that service (not cheap "no-hubs" from the ubiquitous orange big box). 
We call them "mission bands" but that is a brand name (no endorsement) that has become a common moniker.
Of course, you should check with your local code enforcement authority.