The behavior you are looking for can be achieved with this code (simple version):
using(Mutex mutex = new Mutex(false, "GlobalMutexId"))
{
    mutex.WaitOne();
    //Do your thing
    mutex.ReleaseMutex();
}
Or if you prefer a more reusable approach:
public class MutexFactory
{
    private string _name;
    public MutexFactory(string name)
    {
        _name = name;
    }
    public SingleUseMutex Lock()
    {
        return new SingleUseMutex(_name);
    }
}
public class SingleUseMutex : IDisposable
{
    private readonly Mutex _mutex;
    internal SingleUseMutex(string name)
    {
        _mutex = new Mutex(false, name);
        _mutex.WaitOne();
    }
    public void Dispose()
    {
        _mutex.ReleaseMutex();
        _mutex.Dispose();
    }
}
Can be used like this:
private void TestFunction()
{
    MutexFactory factory = new MutexFactory("YourMutexId");
    for (int i = 0; i < 100; i++)
    {
        // also works for new instances of your program of course
        new Thread(Interlocked).Start(factory);
    }
}
private void Interlocked(object obj)
{
    Guid guid = Guid.NewGuid();
    MutexFactory factory = obj as MutexFactory;
    using (factory.Lock())
    {
        Debug.WriteLine(guid.ToString("N") + " start");
        //Waste Time
        Thread.Sleep(50);
        Debug.WriteLine(guid.ToString("N") + " end");   
    }
}