Record input twice, muting at certain times for one

Sorry if the title is a little convoluted, it’s the best way I could describe it. What I want to do is to record from one input into 2 different tracks at the same time and being able to mute one track at times while the other stay recording.

No you can’t do that, but you can make a copy after recording and then edit one of them.

Do you want to end-up with two separate recordings, or a stereo recording with different left & right channels? Something else?

If you have a stereo interface (or USB mixer) you could turn-down the (hardware) gain knob to mute one channel/during recording. (If you have one microphone/source with a 2-input interface you’d have to split the signal an run it into both inputs. With a mixer you can use the pan-pot and the master left-right controls.) But, it’s easier to do it in post production.