We need to specify --routines to take backup of stored procedures with data and tables.

The following command will take backup of entire database including stored procedures. For example, your database name is “mydb”.

mysqldump -u root -p –routines mydb > mydb.sql

To take backup of only Stored Procedures and Triggers (Exclude table and data ) use the following command.

mysqldump –routines –no-create-info –no-data –no-create-db –skip-opt mydb > mydb.sql

Reference:
https://tecadmin.net