This is a poor method of jointing and not to be be recommended for strucural
work as it significantly weakens the whole job.

Bollox. Utter bollox.

Yes and no. In the OP's application he may be looking to raise a floor level, and structural strength of the new timbers is not important.

However timbers with a strength rating (C16, C24) can't be be cut down and the rating automatically maintained.

E.g. If you cut a 50*200mm C16 rated beam, you can't get 2 beams of 50*100mm rated at C16.

You *may* do, or it may be that the structural strength was concentrated in one side and the other has a significant defect within the timber.

(there's also a formula for de-rating for notches)