Before we get down to the nitty gritty of actually leaning to growl, you need to listen and learn from some of the great proponents. This was originally one of the many saxophone
effectsoften 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.
In the soundfiles listen to how Ben Webster uses varying degrees of growl, and how Lee Allen uses it on only the first couple od notes to make an opening statement. It is very effective to use any effect in this way and not necessarily as a permanent part of the sound which can lessen its impact.
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 note 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