I have a big bag of potatoes I bought that aren't organic and I didn't eat all of them. They have reached a point where they really aren't worth the trouble to use for food. Can I cut them up and use them to fertilize/mulch my organic garden without contradicting USDA Organic standards? It would seem like such a waste to simply throw them in the trash.
Specifically to the point of what you can do while complying with the relevant USDA Organic standards (and disregarding what might be a "good idea" or "fine with you or me"):
You cannot apply them directly to your organic garden without contradicting the USDA Organic standards ((c)(3) - "in a manner that does not contribute to contamination of crops, soil, or water by ... residues of prohibited substances").
You cannot compost them and apply the compost to your organic garden without contradicting the USDA Organic standards ((d)(1) - "The producer must not use ... Any ... composted plant ... material that contains a synthetic substance not included on the National List of synthetic substances allowed for use in organic crop production").
You may compost them, apply the compost to a non-organic biomass production system (for example, sod/hay), cultivate that non-organic biomass production system for three years in a manner which allows you to transition to organic biomass production at the end of that period, then apply biomass collected from that system to your organic garden (either directly as mulch or after composting). (This is harder to cite: essentially, but the idea here is that you can use them as a non-approved input and then spend the three years converting to Organic, then use the output - which is Organic - as an approved input.)
They'll just rot on the ground so not useful for a mulch.
Just put them into your compost bin, or bury them so that they might sprout for the next season though many store bought spuds are treated with sprout inhibitors.
No!!! I guess you live in the US, right? None organic food is heavily contaminated with pesticides and probably genetically modified. Not a proper addition to compost for organic gardening.