You may only vote by mail in Texas if 1) you are age 65 and older; 2) you have a disability; 3) you are expected to be out of the county of your residence or the country; and 4) you are in jail. An application for a ballot by mail is available online at https://www.sos.texas.gov/elections/voter/reqabbm.shtml. Print and complete the form, then mail it to the early voting clerk in the county where you vote.
Some county early voting clerks are even offering an opportunity to email early voting applications to the clerk. Mansfield is located in three counties so residents here will need to contact the election office in the county where they reside.
Johnson County: https://www.johnsoncountytx.org/departments/elections-office
Ellis County: https://www.co.ellis.tx.us/312/Elections