Hi J.. Our 2.5 yr old son has speech delays and is getting therapy too. His tantrums aren't as bad or as frequent now that we've started doing the following:
I tell him a few minutes before we need to stop playing or before mealtime, etc. and I'll do a 3 minute warning, a one minute warning, then I'll say, ok it's time. I also do that when giving him a food he really likes - I say, just two bites left, ok last bite, all gone. It gets him prepared.
We work on his vocabulary and model easy words, prompt him to repeat us with "You say..." Even if he gets a close approximation, like Peas for Please, it's good enough for now. I look at him when he's trying to tell me something, because sometimes he'll point, use baby sign language, etc. and that helps me if I can't understand his words. In the car he always shouts "more!" and I have to look to see he's pointing at the radio to know he wants me to turn on the music.
If I can't figure out what he wants, I try the "Happiest Toddler on the Block" method of mimmicing his tone and saying, "You want it! You want it now! You're mad! But I don't understand so we'll have to wait." Then I try to distract him with something else that he usually likes, like his Teddy Graham treats or some singing. Sometimes it works, sometimes it doesn't.
If he's really upset, I'll try some massage or compressions, where I give him bear hugs and hold his arms to his body for a minute. Sometimes I whisper that I love him or sing a gentle song while I'm doing this. It often calms him down after a little while. You can also look into ear pulls and ask his speech therapist about it. I don't want to try to explain it here and have you do it wrong, but it helps with some kids.
As far as discipline when I know he understands me but just won't stop fussing, I'll do a slow count from 1 to 3. I'll say, "I need you to stop fussing/throwing/hitting by the time I count to 3. 1.... 2.... 3." We do this often enough that he usually stops the behavior by the time I get to 2. If he won't stop, I say, "ok, you get a time out." And I take him to the corner for a couple of minutes. If he's upset, this quiet time seems to help him collect his thoughts. If he's in a silly or naughty mood, he may not take it seriously and smile the whole time. If he comes out of time out and does the behavior again, he goes to his room for a few minutes.
Good luck! Hope some of this helps.