Assuming that the domain is a single word domain like gmail.com, yahoo.com, use
select (SUBSTRING_INDEX(SUBSTR(email, INSTR(email, '@') + 1),'.',1))
The inner SUBSTR gets the right part of the email address after @ and the outer SUBSTRING_INDEX will cut off the result at the first period.
otherwise if domain is expected to contain multiple words like mail.yahoo.com, etc, use:
select (SUBSTR(email, INSTR(email, '@') + 1, LENGTH(email) - (INSTR(email, '@') + 1) - LENGTH(SUBSTRING_INDEX(email,'.',-1))))
LENGTH(email) - (INSTR(email, '@') + 1) - LENGTH(SUBSTRING_INDEX(email,'.',-1)) will get the length of the domain minus the TLD (.com, .biz etc. part) by using SUBSTRING_INDEX with a negative count which will calculate from right to left.