Exceptional means outstanding, extraordinary or even unusual. So, we can say:
a) He is an exceptional singer.
b) The jury needs to take into account the exceptional circumstances in which the crime happened.
Exceptionable means offensive or objectionable.
1) His reply was exceptionable. Everyone else walked out of the meeting.
2) The songs of this movie are highly exceptionable.
Several words related to exceptional/exceptionable are quite in use and it would be useful to look at them:
Unexceptionable means something which is difficult to find a fault with. For example:
1) The lawyers logic was unexceptionable. The judge had to agree.
Another related usage is, ‘taking exception’ which means taking offense.
Thus, you can say, “I take exception to this argument. You cannot generalize”
In summary, exceptional = extraordinarily great, exceptionable = offensive, objectionable.