Your route map is probably something like this:
routes.MapHttpRoute(
name: "API Default",
routeTemplate: "api/{controller}/{id}",
defaults: new { id = RouteParameter.Optional });
But in order to have multiple actions with the same http method you need to provide webapi with more information via the route like so:
routes.MapHttpRoute(
name: "API Default",
routeTemplate: "api/{controller}/{action}/{id}",
defaults: new { id = RouteParameter.Optional });
Notice that the routeTemplate now includes an action. Lots more info here: http://www.asp.net/web-api/overview/web-api-routing-and-actions/routing-in-aspnet-web-api
Update:
Alright, now that I think I understand what you are after here is another take at this:
Perhaps you don't need the action url parameter and should describe the contents that you are after in another way. Since you are saying that the methods are returning data from the same entity then just let the parameters do the describing for you.
For example your two methods could be turned into:
public HttpResponseMessage Get()
{
return null;
}
public HttpResponseMessage Get(MyVm vm)
{
return null;
}
What kind of data are you passing in the MyVm object? If you are able to just pass variables through the URI, I would suggest going that route. Otherwise, you'll need to send the object in the body of the request and that isn't very HTTP of you when doing a GET (it works though, just use [FromBody] infront of MyVm).
Hopefully this illustrates that you can have multiple GET methods in a single controller without using the action name or even the [HttpGet] attribute.