This was originally one of the many saxophone effects
often used as a novelty. Apart from the fact that it is now one of the main hallmarks of rock and blues saxophone playing, it was also used in mainstream jazz: notably Ben Webster, Illinois Jacquet and Earl Bostic. Charlie Parker also growled on occasions as did avant garde pioneers John Coltrane and Archie Shepp.
The saxophone growl is made by singing or humming a note at the same time as playing. This note is not necessarily the same note as you are fingering/playing. The ideal note to sing can vary, it could be a harmony note or the same note slightly out of tune.
I find the best way to practice this is to play a note, then hum any old note in the back of your throat. Alter the pitch of this hummed not until the interference with the saxophone note creates a good growl
Then go slowly up and down the chromatic scale doing the same on each note. You will gradually get a feel for which note to sing or hum, and after a while you should be able to do this without thinking about it