The answer is more complex than one might think at first reading. At first glance, one might respond that the beneficiaries don't "inherit the debts" of the Trustor of a revocable trust upon death of the Trustor, and that is technically true. However, the real property is the collateral for the secured loan, so it will pass to the beneficiaries who are to receive it subject to that security interest. If the debt exceeds the value, than the beneficiaries have received nothing of value at the time.
That is the easy part. Next, consider the nature of that secured indebtedness. Was it a purchase money borrowing for a primary residence, less than four units in size? If so, the anti-deficiency judgment legislation may extinguish the debt, upon non-judicial foreclosure of the property. But if this is a full recourse debt (meaning it is a debt that you owe and is not subject to such statutory protection, you or your estate or your trust, as your successor-in-interest, could be called upon to pay the deficiency. That means that OTHER assets in the trust estate could end up liquidated to pay-off the debt. In that way, the debt impacts your beneficiaries due to them inheriting less of other properties. Don't be overly-alarmed, though, if this is a typical mortgage on a primary residence, single family home, and it is a purchase money loan (not a HELOC or refinance with money having gone-out to you), then it is likely subject to the anti-deficiency judgment rules.
Deeding the property out of the trust won't change the exposure to a deficiency judgment, if any exists, since you made that debt and your probate estate and secondarily your revocable trust's estate, are responsible for your debts.
I suggest that you consult a local real estate attorney who understands secured creditors' rights, and try to work out a short sale if there is some concern about deficiency judgment exposure. There is currently some new statutory protection for the phantom income previously associated with discharge of indebtedness transactions, and that attorney should be able to help you with understanding those rules.
Before I answer, I need to make a couple of assumptions. First, that the "trust" you are referring to is a simple revocable living trust (i.e. one that currently holds title to your assets, of which you serve as trustee and is revocable or amendable by you at anytime). Second, I am assuming that your "mortgage" is a standard bank type loan secured by a Deed of Trust.
No, do not take your property out of trust.
In California it does not matter if your house is in or out of your trust, the house remains as collateral for the loan ("mortgage"), Taking it out of the trust would only result in it being probated adding additional costs and hassles to your heirs.