How can I make my follower cut it out with all the jibber jabber?
Solution 1:
You can't politely ask favors of your followers, so turn your Voice Volume to zero instead.
I thought I'd miss the dialogue, but, after several playthroughs, I haven't changed it back.
Solution 2:
No, there isn't. Blizzard has aimed to make the controls for Diablo as simple as possible, so omitted a lot of options that might have been useful. Your only option is to not adventure with a follower in tow.