I would just activate woodcutting labor for the dwarf with the axe...
it isnīt as if woodcutting took a long time, or that the logs would have a higher quality if hewn by someone with a high skill level
That's true, but a statue will have a higher quality if created by a mason with a high skill level, so will a rock table, and the same also goes for anything that comes out of a mason's workshop.
Thatīs why I would balance it out with the dwarfs mason duties...
like:
Fell 3-4 trees (so that the carpenter has work), afterwards return to your duties as mason.
(In my games however I evade this problem altogether by bringing 30-40 logs of fungiwood with me,
often I donīt have to fell a single tree, because afterwards I can supply my industry with enough wood
just by buying it from the trading caravans)
Designate an activity zone as a garbage dump, then {v}{i} on the dwarf with the axe, {+}/{-} to the axe, {enter}{d} to designate the axe to be dumped (make sure it's not already {f}orbidden. Then, once it's dumped, unforbid the axe and hope the mason doesn't grab it again.
Neither forbiding or dumping make her loosen her grip.
But in any case, a bunch of mountain gnomes turned up and drunk all of my fortress' booze, effectively killing the fortress. Reclaim time!
Gnomes, monkeys and Buzzards are the creatures in 0.31 who taught me,
to put my food and booze into intermediate stockpiles in my mines (usually just a hallway designated as such a stockpile) as soon as possible