Solmaz, how big is "big?" And how are you doing backups?
Whatever you decide to do, make sure to create a backup of your Moodle before doing anything. The suggestions by Leon and C Behan are good. However, they might "modify" data that may prevent you from doing course analytics in the future, if this is important to you.
Many years ago, I had a problem with a database that grew to be so big (1GB) that my
server company said I needed to upgrade to a VPS. I did that, and it solved my database-size problem. It also improved my Moodle's overall performance, including backups.
By the way, my "backup" method is to backup the database via the
MySQL command line, like this:
mysqldump -uyour_database_user -pyour_password --opt -r$your_server_location/backup_moodle/NOW-moodledb.sql your_moodle_database_name
My backup of the database is currently 2.5GB for around 50 courses, around 2000 students. My moodledata backup is around 10GB. Yep, I run a relatively small Moodle.
I do have two backup Moodle's, one for Moodle 1.9 and one for Moodle 2.9, that are not mixed into my current Moodle. I can access data from these older Moodles via my sandbox
MAMP. As you might guess, I will probably begin a new Moodle when Moodle 4.0 comes out, and then move my current Moodle3 to my MAMP.