SQL Server Audit file
SQL Server Audit logs to either a binary file or Windows Application log or Windows Security log.  There are different options for reading the output depending on where you have logged to.  If you are logging to a binary file you could create a simple process that reads it with sys.fn_get_audit_file and outputs to a readable textfile, eg using SSIS, use an 'Execute SQL' task to run the following SQL and pipe the output to a text file:

SELECT *
FROM sys.fn_get_audit_file ( 'X:\SQLAudit\yourAuditName_*.sqlaudit', DEFAULT, DEFAULT );


You will need some way of tracking the files you have imported/exported so a simple table would help there.

A quick google shows someone else has done something similar with Powershell here.