First note that bitcoin nodes pass on blocks. So even if most machines in a country are cut off from the rest of the world it only takes one machine that can "see both sides" to keep the blocks flowing back and forth.
But what happens if an area is completely cut off from most of the world?
Miners on both sides of the cut will continue trying to find blocks. The probability of them finding them is determined by the current difficulty.
Assuming the "most of the world" side has most of the hashing power it will continue more or less as usual.
The "armenia" side on the other hand will experiance a massive drop in block rate. If they have 1% of the hashing power (and I doubt they have even that) then they will experience a one hundred fold drop in block rate.
If the isolation goes on long enough then the "target" on the "Armenia" side will adjust to restore the normal block rate but this will take a long time. The "target" only readjusts after every 2016 blocks and it only readjusts by a factor of up to four each time. Say that when the split happens we are halfway between difficulty readjustments, if the "Armenia" has one percent of the hashing capacity then it will take about 100 weeks (~two years) to reach it's first difficulty adjustment.
If and when connectivity is restored then any blocks mined on the "Armenia" side will be discarded as the chain from the "rest of world" side is much stronger. Transactions from the "Armenia" side may be re-included in new blocks if they are still valid.