Or you could just use Tor.
Block access entirely? Only if they were willing to stop all communications and travel in/out of the country. You could carry keys on paper and instructions in your head and apply them on the "free side" of the border. I don't think it's practically possible to entirely prevent such transactions. You can make them illegal; you can make them difficult; you probably can't stop them as an individual country.
Blocking based on traffic analysis is easily bypassed by using a VPN/tor
That means raiding mining farms while limiting their number by limiting the size of Bitcoin.
Its only something the US or China could do.
Otherwise no, there is no way of completely blocking it. There are ways of making it impractical for the vast majority, though.
Is there way to continue using your Bitcoin in this case? Or is it effectively the same as having a bank account frozen (i.e. you can't conduct any transactions if you don't have broad connectivity).
Or am I misunderstanding something fundamental? (I realize it's probably not a single domain/endpoint like other sites I referenced, but the traffic probably has other characteristics that would make it easy for a state to disable).