No. Working as a special prosecutor means that on a specific case, the DA's office had a conflict and got an outside lawyer - a criminal defense lawyer - to handle the prosecution of that case. Generally that means that the DA's office respects that lawyer and the lawyer's integrity. Logically, such is more likely to have a positive impact on the judge as well. (Seemingly the DA & judge would rely more on the lawyer who they accept as a special prosecutor....)
Without some evidence of HOW this hurt you - made the results of your trial not trustworthy - then this is no issue.
YOU don't request a mistrial; your lawyer does - and only DURING the trial because of an issue that arises or comes to light. Are you in trial?
If your case is actually still in process in court, you can always hire another lawyer to substitute in to represent you - but you should consider whether that is really helpful to you.
If you have been convicted, you need to be hiring an appellate lawyer to appeal your case. Let that lawyer know your concerns.
The fact that an attorney works as a special prosecutor and a defense lawyer does not pose an ethical problem as long as there is no overlap as far as clients, witnesses, etc. I do not see this as a basis for a mistrial.
This answer is provided for educational purposes only and is not intended as the practice of law in any jurisdiction in which I am not licensed. The answer does not constitute legal advice nor does it create an attorney-client relationship. The answer is based only on the information provided, and may be inaccurate in the context of additional facts that have not been provided. The questioner should be aware that I am only licensed to practice law in the state and federal courts of Minnesota. Accordingly, before taking any action or refraining from taking any action, the questioner should consult with an attorney licensed to practice in his or her jurisdiction.
Attorney Henley is right on the money. The District Attorney's Office will appoint competent and capable lawyers as special prosecutors. You are likely in very good hands with the defense attorney you currently have. However, you have the right to hire a different lawyer if you choose. Speak with the attorney you have about your concerns and he or she will be honest about what effect, if any, the special prosecutor assignment may have on your case.