.speakingdone is not a property, it is an event. Under the code window, select the TTS control in the top-left dropdown (in your case it is called spkSpeak, the "Text To Speech" control). Then look at the list in the right dropdown; you'll find a whole bunch of events that are automatically called when different things happen. SpeakingDone and SpeakingStarted are the two obvious useable ones.
When you select SpeakingDone from that list, you'll get this:
That sub will call when the voice is done speaking...drop your mute command in there and you're done.
Private Sub spkSpeak_SpeakingDone()
EDIT: I took another look at this and it appears we were working with two different versions of the text-to-speech OCX - my SAPI4 installed two different OCXs. I was looking at the events of the TextToSpeech one and you seem to be using the DirectSS one. The good news is it still works, but the event is called AudioStop instead of SpeakingDone. Same thing, it's an event - set up the sub in the code. I just tried it - I sent some speak to it and the instant it finished speaking it called the AudioStop event.
Something like this:
Private Sub Command1_Click()
' MUTE THE WMP HERE
DirectSS1.Speak "hello hello hello hello hello"
Private Sub DirectSS1_AudioStop(ByVal hi As Long, ByVal lo As Long)
' UNMUTE THE WMP HERE