It would be pretty hard
With a sub or divers. But with a dedicated ROV + custom tooling you'd be able to do it in any depth.
Remove the armouring at 2 points with a grinder (standard practice when cutting ROV umbilicals, which are km-long kv-carrying electric/fibre cables, and easy enough to automate)
Surround the 2 sections in oil, held very slightly above ambient pressure (cheap to do)
Abrade away the plastic sheath around one conductor. The oil prevents it shorting to seawater. Connect to it a surface-mounted jumper wire. Repeat for the other conductors.
Repeat at the second position, and join the jumper cables in the middle with a wet splice. Et voila, you've got a jumper for the power. You can now cut the conductors somewhere in between them and, so long as your jumper is correctly specced, no-one will know.
So you cut and intercept the fibres at your leisure. Fusion splicing is quick and cheap (well, sub-10k for a small unit. Cheap on a SpecOps budget) and introduces very low losses. Pass your data down the adjacent fibre you rent on this cable, or take your fibres off as single strands (so they'll snap off if the cable is recovered, with the remains hidden under marine growth).
Re-seal the cut-apart section and re-lay everything layer by layer.
Remove the power jumpers and relay the armouring, welding the ends back together.
The whole operation could take a few minutes with appropriate automated tooling and practice. The total disruption to the fibre could be under a minute with appropriate planning and equipment.
Even manually, reterminating armoured subsea umbilicals like this can be taken down to well under an hour if you're using a fusion splicer for the fibres. It's essentially the same process except without the power jumping (as it's turned off at the time).
Do it close to a booster and a cable guy onshore with an OTDR would barely notice.
It's not just possible that they could have done it, it's plausible that they do it semi-routinely.