If you are watching your own stream, make sure you mute the stream in Twitch. If you are in a Skype call or talking to someone some other way via voice chat, and they are watching too, have them mute it as well.
Actually, if this is not a problem. I know exactly what you are talking about because I had the same issue. In Settings, you can choose your mic. Go ahead and pic that mic. Say it was a webcam mic; if you add the webcam as a Source, then in the properties of that Source, mute the audio of it. If it is not a webcam and just a normal mic, the keep it in the settings, except, mute the mic on OBS Control Panel.
OBS is picking up your mic twice, so just mute one of them.