Here we force Rapise to ignore actual result of the DoExecute by calling Tester.SuppressReport.
Tester.SuppressReport(true);
var res = VerifyResponse_New_Request.DoExecute();
Tester.SuppressReport(false);
// Check 1: Check that response is failed with specific error code
Tester.AssertEqual('This request should fail', res, '400 Bad Request');
// Check 2: Check that response just failed
Tester.Assert('Response failed', VerifyResponse_New_Request.GetResponseIsErrorStatus());
So we ignore the call itself, but then use the results of the call in a way we need. Just don't forget to re-enable the reporting by doing Tester.SuppressReport again with false.