If you are thinking of using the PICAXE as an audio recording and playback device it will not be possible to do that by itself although it could control audio recording and playback devices.
If you wish to have the PICAXE respond to audio activation ( hand-clap, whistle ) that would be possible with a suitable amplifier and detector circuit. Voice recognition could also be possible with suitable external hardware but the PICAXE cannot do that by itself.