Although skin doesn't 'breathe' and can't be 'suffocated', excessive amounts of mineral oil can prevent it from performing effectively; the skin also receives its oxygen supply via the blood stream, so this is more of a nourishment and hydration issue. As a natural side effect, mineral oil is also comedogenic; this means it can block pores and cause blackheads or acne, as the skin can't rid itself of bacteria or dead skin cells. If you suffer from breakouts or are prone to acne, it may well be worth ridding your cosmetic repertoire of any products that contain mineral oil to ensure your skin has a fighting chance. The substance will sit over the surface of skin and prevent the natural 'shedding' and renewal process that rids itself of dead skin, bacteria and anomalies that can cause big ugly spots. In order to minimise blocked pores that become infected and result in pimples, the skin must be able to regenerate as easily as possible - mineral oil simply hinders this process.
In 2015 we now have so many better alternatives to mineral oil that don't cost a fortune to include; in my opinion a lot of companies continue to use mineral oil because it's cheap as chips and bulks out a product. If you continually use products with mineral oil in over time then the result could be dry, tender and flaky skin as the surface level can't attract and therefore retain moisture. However, mineral oil doesn't 'suffocate' skin cells as is widely reported, nor will it 'poison' cells because it's so closely related to petrol. Many 'natural' companies choose to pick on ingredients and identify them as bad for you as a way to promote and push their organic alternatives, so it's important to make purchasing decisions that are right for you and your skincare routine.
Are you concerned about using mineral oil, or is it just another ingredients that's been getting a bad rep?