What is "chopsing the ref"?

Solution 1:

OED has this definition (sense 8) for chop...

trans. To exchange or bandy words; esp. in to chop logic;
to exchange logical arguments and terms, bandy logic, reason argumentatively, argue.
(In late use, often erroneously referred to chop sense 1, as if to mince, divide minutely, split hairs, or hash up.)

So etymologically it's not related to chop (usually pl. Jaws; sides of the face), which is from chap. Nor is it very closely related to chop = cut up, as OED points out above.

Regardless of whether the variant chopsy derives from the "bandy words" or "mouth/jaw" sense, there seems no doubt it's originally/primarily Welsh. Here's an early instance from Welsh Author Ron Berry in The Full-time Amateur (1966)...

"Just let him know ... and don't be so bloody chopsy, ah, if you don't mind?"

Julie Coleman in The Life of Slang (2012) includes chopsy in a list of "slang terms originating or chiefly used in Wales", and this website locates it even more precisely in South Pembrokeshire (the South-Western tip of Wales).

Solution 2:

Since "chops" can be slang for "mouth" (see Collins), it makes sense that "chopsing at" would be synonymous with "mouthing at."