My question is:

My wife up and left the house a month ago and refuses to explain her reasons for doing so. She has claimed that she want to work things out but instead I get divorce paper work 10 days after she has left. She is currently living with my brothers ex-wife and is going out with several other people "friends that she has no intimate feelings for she claims" and is not coming home to the place she is staying at currently. I am not being bitter but if I haven't responded yet to the paper work and she is indeed with another man is that claimed cheating since she has filed?

Welcome to AMHD; most of the time, a party's conduct after the separation is not relevant to the issues in a divorce; however, it could have some bearing on child custody and visitation.

Maybe I didn't do a good job of explaining it. If I just received my summons or notice she has filed for divorce and she is sleeping with some one else is that considered cheating. I still have 13 days to send in my paper work before anything else takes place. So again if she is caught does the court see that as abandoning the relationship or is it permissible to carry on in that matter?

I believe you explained very well, that your wife left the house a month ago, which would probably be the last possible date for the 'separation', which must be alleged in the divorce petition. Her behavior since the date of separation would not be considered cheating, as far as I am aware. If you can prove this relationship began prior to the separation, then you might have something to go on. Just curiious: what is the ground, or grounds, for divorce?

I wish I knew as well to be honest with you. It clams parties are incompatible with one another. Which is unusual to me because we have not had an argument that has lead either of us out of the house hold. Nor have we ever had a disagreement that has been heated. I have tried to replay every situation I can and nothing makes sense. I am not in denial either and I can handel things if there is an honest to goodness explanation. Others tell me it could be due to my income (which is high). She has never been that way though.

"Incompatible" sounds like a 'no fault' ground, which means, usually, that she can get the divorce whether you agree or not if she testifies that the marriage is irretrievably broken, with no hope of reconciliation; or words to that affect. Did she allege a date of separation? Do you have any evidence of cheating before the date of separation? Is she asking for alimony?

All I have is a page that states EX PARTE TEMORARY ORDERS page dated 1/27/09 giving me temporary use of home and autos along with other businesses I own. So I don't really know what that means. It also states that the petitioner is partially dependent on the respondent for her support. As for the cheating no evidence of that until after I received the paper work.

...It also states that the petitioner is partially dependent on the respondent for her support. As for the cheating no evidence of that until after I received the paper work.
My hunch is that your wife has an attorney, which means you need one also. The allegation that "petitioner is partially dependent on the respondent for her support" portends a claim for alimony. Adultery is generally a defense to a claim for alimony, so you need to decide how you want to proceed. If you have no knowledge of her behavior prior to the separation, you may want to retain a private investigator. You need a lawyer.

In the State of Mississippi

In the State of Mississippi where I live, you are still considered married until you get the final divorce papers after court. If you sleep with someone outside the marriage before the divorce is final you are still committing adultery. I would suggest you check the laws concerning adultery where ever you are located. You can do a search on the internet for the laws for your area. I didn't catch my wife until she left.