I just looked to be sure, and my SR-specific med info sheet says not to "chew, cut or crush". So best course of action would be to ask your pharmacist.

My SRs are also hard tablets, mossanimal. Have you ever used a pill identifier (not as replacement for checking with your pharmacist)? Such as https://www.drugs.com/pill_identification.html

Mine are purple, round and have an imprint of IG 485 (IG is on one side, 485 is on the other, but it's all just called the imprint.) Punched in, what comes up is:

"Drug: Bupropion Hydrochloride Extended-Release (SR)
Strength: 150 mg
Pill Imprint: IG 485
Color: Purple
Shape: Round"
The manufacturer of my generic (currently anyway) is Cipla.

The other interesting thing is that they refer to it as an extended release. Extended release meds usually have XL. Of which there is also in bupropion. Digging further, my med info sheet (from pharmacy) refers to them as "sustained release". No doubt more accurate if we consider the spelling. And on this sheet it says not to split. Even though it's not strictly an extended release. It's between an extended and an instant release (I don't know if it even comes in instant(?))

Asking the pharmacist is looking pretty good, eh?
(I'd skip the doc and go straight to a pharmacist for this stuff.)