Морда (грубое) - лицо. Подставлять - делать доступным для удара, to expose, to put near. Seems like the author of this saying says another person is doing something that makes the author of the phrase want to hit them. Or they do something that makes their face available for another action like this. :)

You were better if chopping wood, than putting your muzzle. Counter-question: where is a muzzle put?