WASHINGTON—Democratic presidential candidate Beto O’Rourke and his wife, Amy, appear to have underpaid their 2013 and 2014 taxes by more than $4,000 combined because of an error in the way they reported their medical expenses, according to tax returns the couple released Monday evening.

They took deductions for those costs without regard to the limit that only allowed that break for medical and dental expenses above 10% of income for people their age. Had they not taken the nearly $16,000 in medical deductions, their taxable...