I want to stop the actions that are called by the jQuery.ajax method on the server side.
I can stop the Ajax request using $.ajax.abort() method on
You may want to look at using the following type of controller Using an Asynchronous Controller in ASP.NET MVC
and also see if this article helps you out as well Cancel async web service calls, sorry I couldn't give any code examples this time.
I've created an example as a proof of concept to show that you can cancel server side requests. My github async cancel example
If you're calling other sites through your code you have two options, depending on your target framework and which method you want to use. I'm including the references here for your review:
WebRequest.BeginGetResponse for use in .Net 4.0 HttpClient for use in .Net 4.5, this class has a method to cancel all pending requests.
Hope this gives you enough information to reach your goal.