Guess that physician hasn't figured out Fick's law yet. What a bonehead.
General observation: You should never (and yes, never) cut a transdermal patch as it really does affect drug delivery in really unpredictable ways. Open your Ansel's for why, but there's some real controversy over the years over the effectiveness of transdermals on different skin thicknesses much less cutting the system open. However, it is possibly safe to cut certain topical patches that only have epidermal or up to dermal release (so lidocaine and other topical pain relief may be cut given the package insert instructions) as there is no systemic release and that the drug does not well up.
And
@idiot, I hope you're recovered some sanity and morale from being overexposed to drinking from the UF firehose.