Can I shutdown my mac for more than 6 months without damaging it?

I see no issue.

That should not be a problem.

If the unit is more than four years old, the internal clock battery may need replaced

once you go to start up the computer again, since that stores data in PRAM chip

that needs powered by a tiny battery inside the computer. An Apple Store Genius, or

if not, an AASP (authorized service provider) would be able to replace that battery.

Otherwise, the clock, date and day etc may need to be reset. If you have the network

time server (where you're moving to) set correct for your time zone & region, then it

would load the corrected time. Otherwise, you'd have to change it. Other applications

or cloud based software may also see the old time zone, even though you've re-set it.

Hopefully your Mac enjoys the 'mini vacation' and starts up as it should later on...! 🙂

If the computer is plugged into a power source but not powered up that will keep the battery charged. The computer does not need to be turned on in order for the charging to occur.

In this instance, since the original post question implies a move, perhaps storing the computer

for up to six months before using it again, I had to take the leap of faith to suggest the worst

case scenario, as o.p. said: if I can keep it shut down and not use it for more than 6 months

{With two build versions of Mini here, I am aware of the details.

Plus a few other Macs sitting around twiddling their keyboards...}

With an open-ended statement, such as that, I'd suspect a storage locker or moving company

may not allow you to keep stuff plugged into your packing box even if equipped with power port.

Though I'd want mine to be plugged into an uninterruptible power supply, while in storage, too. 😝

To be safe, I would get some sort of sealable packaging to put the Mini

into. Before sealing it, make sure you put in along with it several packs

of silica gel to absorb any moisture when it is sealed.

You would also need to insure that the storage location will not exceed the

storage temperature specs.

Following this, storing for 6 months should be no issue.

For some, more than a few words are Too Much Information...🙂