The person who co-signed my auto-loan has died. How can I remove them from the note?
If this is a co-signer on a loan, then it doesn't really matter. If this was a co-owner on the title (as Dilip Sarwate and you indicate in comments to the question), then it may or may not matter.
If you owned the car in joint tenancy (i.e. with right of survivorship) then you may not need to do anything. It would be your car with no need to be probated or go through a trust. Some states automatically treat cars in this fashion. Other states may include ownership details on the title or make forms for survivorship agreements. If the deceased was a spouse or perhaps a child or parent, then your state may have a rule that presumes survivorship.
If the ownership is unclear because either you failed to properly specify survivorship or because your state doesn't have a survivorship rule, then you may need to determine what happened to the deceased's estate. If there was a will, the deceased may have purported to bequeath one half of the vehicle. If there was no will, then the deceased died intestate and it would go through that process (typically, the intestate share will go spouse, children, or parents).
Once you ascertain who owns the car, this may be as simple as following the DMV process in your state for re-titling a car. (Example: Illinois DMV re-titling upon deceased co-owner).
Of course, speaking pragmatically, if nobody is making noises about taking your car, then I'm not sure you need to be too finicky about crossing the Ts and dotting the lower-case Js. My understanding is most states allow auto title transactions without the signature of all co-owners. Failure to properly tidy this issue could put your vehicle in legal limbo (e.g. when somebody claims to own half of it), but it may also never come up if nobody realizes there's anything to dispute. Pursue the legal and ethical niceties to your comfort level.