See this piece of code I have written for you to remove the Duplicate nodes from XML.Run the code as it. ( I have extended your xml a bit to see proper result)

        string myXML = "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"yes\"?>"+
                        "<NewDataSet xmlns:xsi=\"http://www.w3.org/2001/XMLSchema-instance\">"+
                            "<ProdSheet>"+
                                "<ProductId>851</ProductId>"+
                                 "<BaseSku>ACCJVC01</BaseSku>"+
                                 "<Name>JVC GUMY In-Ear Headphone with Colour Cord (Mint Blue)</Name>"+
                             "</ProdSheet>"+
                             "<ProdSheet>"+
                                 "<ProductId>852</ProductId>"+
                                 "<BaseSku>ACCJVC01</BaseSku>"+
                                "<Name>JVC GUMY In-Ear Headphone with Colour Cord (Black)</Name>"+
                            "</ProdSheet>"+
                            "<ProdSheet>" +
                                 "<ProductId>852</ProductId>" +
                                 "<BaseSku>ACCJVC01</BaseSku>" +
                                "<Name>JVC GUMY In-Ear Headphone with Colour Cord (Black)</Name>" +
                            "</ProdSheet>" +
                            "<ProdSheet>" +
                                 "<ProductId>852</ProductId>" +
                                 "<BaseSku>ACCJVC01</BaseSku>" +
                                "<Name>JVC GUMY In-Ear Headphone with Colour Cord (Black)</Name>" +
                            "</ProdSheet>" +
                            "<ProdSheet>"+
                                "<ProductId>853</ProductId>"+
                                "<BaseSku>ACCJVCHAF130DE</BaseSku>"+
                                "<Name>JVC GUMY In-Ear Headphone with Colour Cord (Orange)</Name>"+
                            "</ProdSheet>"+
                        "</NewDataSet>";

        XmlDocument xDoc = new XmlDocument();
        xDoc.LoadXml(myXML);

        XmlNodeList xNodeList = xDoc.SelectNodes("NewDataSet/ProdSheet");
        string[] keyValue = new string[xNodeList.Count];
        int count = 0;
        foreach (XmlNode xNode in xNodeList)
        {

            foreach (XmlNode xNodeInner in xNode.ChildNodes)
            {
              
                if (xNodeInner.Name == "BaseSku")
                {
                    keyValue[count] = xNodeInner.InnerText;
                    count++;
                    //Here we gather all the Values from the element -BaseSku in a string Array.
                }
            }       
        }

        foreach (string strIfDuplicate in keyValue)
        {

            XmlNodeList xNodeCheck = xDoc.SelectNodes("NewDataSet/ProdSheet[BaseSku ='"+strIfDuplicate+"']");
            if(xNodeCheck.Count >1)
            {
                for (int i = 1; i < xNodeCheck.Count; i++)
                {
                    xNodeCheck[i].RemoveAll();
                }
               
            }
        }

        string outputXML = xDoc.OuterXml;