I use Live with an AXE-FX III as the input and output device. The AXE-FX is also feeding the PA so I don’t want to hear a slightly delayed copy of the external input signal — just the loops when they’re playing. I set the Looper to go into playback mode after recording, not overdub. I set Input -> Output to Never. I set the track’s Monitor to Auto. When doing the MIDI setup I assign the first button on the left to both the Looper “Pedal” (what Live calls it – some people refer to the Big Button) and the track’s Arm button. This way when I start the Looper the track is armed, when I go into Play mode the track is unarmed and the external input is not heard at the output.
This does not work in Clip mode. Apparently the DataLooper does not send a MIDI note or CC message in Clip mode.