How can I remove messages from a queue?

There is no API available to do this. But you can use

• GetMessageEnumerator2() and
• RemoveCurrent(), which also moves the cursor

A benefit of using enumeration is that if a queue has many messages, reading all of them may result in OutOfMemoryException. With enumerator you only read 1 message at a time, and memory allocated for it can be reused.

Another trick to increase performance is to specify which properties to read, so that if the message body is large and you aren't interested in the content, you can disable reading it.

var enumerator = _queue.GetMessageEnumerator2();  // get enumerator
var staleDate = DateTime.UtcNow.AddDays(-3);      // take 3 days from UTC now    
var filter = new MessagePropertyFilter();         // configure props to read
filter.ClearAll();                                // don't read any property
filter.ArrivedTime = true;                        // enable arrived time
_queue.MessageReadPropertyFilter = filter;        // apply filter

// untested code here, edits are welcome
while (enumerator.Current != null)    
     if(enumerator.Current.ArrivedTime.Date >= staleDate)
         enumerator.RemoveCurrent();
     else
         enumerator.MoveNext();

I think you can do something like this:

MessageQueue queue = new MessageQueue(@".\private$\SomeTestName");
var messages = queue.GetAllMessages();
var messagesToDelete = messages.Where(m => m.ArrivedTime < DateTime.Now.AddDays(-1)).ToList();
messagesToDelete.ForEach(m=>queue.ReceiveById(m.Id));

Obviously, you'll have to modify the date stuff to correspond with your scenario.