I think you are supposed to leave it for about 6 weeks after flowering. If it's getting yellow then yes cut it. I sometimes cut it half down if it is getting in the way.

If you want the daffodils to grow again next year, you are better to leave them to die down naturally and not cut the foliage, nor bend it over or tie it up. Once they have finished flowering, give them a general purpose feed, and keep the plants watered. This will put goodness back into the bulb for it to flower again next year. I leave mine in pots at my front door - they look untidy for a few weeks, but they soon die back and I can then remove the dead leaves and pot up with some pansies for the summer. I have been doing this for 4 years now and the bulbs flower each year - good money saving.

If the foliage is really dead it will just come away in your hand... we leave alone and it rots down into the soil.