With no other context, 'No, I haven't gone yet' sounded so odd in my head that I accidentally switched it to 'No, I haven't left yet' despite actually remembering the meaning of mynd. Upon pausing to think, I've decided the reason is I wouldn't use 'gone' in such a sentence UNLESS I included where I haven't gone to, such as 'I haven't gone to the store yet'. If I don't include the place, it's only because it's already been mentioned: 'Have you been to the fair? No, I haven't gone yet.'
Which makes me wonder about the Welsh; is this 'I haven't gone yet' in the sense of 'I haven't left yet', in which case my 'mistake' is probably the preferred translation though not the most literal, or is it 'gone' in the sense of 'I haven't been there yet', in which case 'left' obviously wouldn't work as a substitute for gone. Or does it mean both in a way that doesn't quite work in English? In which case 'left' or 'been' would both work but 'gone' would still sound odd in English.