The government orders the ISPs to cut the connections - how they ISPs actually do it is up to them - whether they power down the routers or simply enable firewall rules.

EDIT: Here's a relevant article by Cloudflare about the Syrian shut-off: https://blog.cloudflare.com/how-syria-turned-off-the-interne...

In small countries, especially in Africa, there might be only one or two Internet exit points for the entire country. It's not like the US where there can be a dozen or two Internet traffic exit points.

ISP are ordered to do so.

You can resist but then there will be consequences...