Can I still use expired petroleum jelly on cuts?

Won't help. Petroleum jelly won't help cuts heal and will not effectively prevent infection. Better for them to be exposed to air, and petroleum jelly blocks it.
You use a Bandaid. You do not use Petrolium Jelly on any cut.First you clean it if it is dirty or contaminated and cover with a band aid.You may use Bacitraci,neosporine or another Antibiotic ointment but keep it covered with a Band Aid.But no Petroleum Jelly expired or not.