Beside from flight, what is next alternative shortest way from Guangzhou to Shantou and how long?

You can take train from Guangzhou or Guangzhou East Station to ST Station, the duration is around 8 hours, and the ticket fare of soft sleeper is CNY246, hard sleeper is CNY167 and hard seat is CNY91.
Ticket fare of the Soft Seat from Guangzhou East Station is CNY137/person.

thanks u for the advice. How about from Guangzhou South train station to Chaouyang train station ? Will this be faster ?

Do you refer to Chaoshan Railway Station? It is located in Chaozhou City, not ST. If you head for that station, you still need to transfer to ST City.