Is the mileage from traveling to care for my elderly mother every weekend tax deductible?

You should check with a CPA for guidance, but there are tax deductions you can get for caregiving out-of-pocket expenses. You want to make sure you do it right, though, so get expert, personal advice from the IRS or a CPA.
Carol

I drive 675 miles twice per year to care for my elderly mother while her caregiver is off. is this mileage deductible?

I'm not a lawyer, so not sure this is correct, but, if she paid your gas, she might be the one to be able to take the deduction as a medical expense. Again, check with a lawyer or accountant.