How can you cut through bones if you don’t have a cleaver?

I'd use a hacksaw.   

If cutting up say a chicken, just slide a knife into the joints to separate. To actually Cut through a bone, use a meat saw or the rednecks way of doing it would be a hacksaw, first sterilized in boiling water. 

Use a saw: a domestic hacksaw works very well and is much better than a cleaver anyway, as cleavers just smash their way through leaving bone splinters.

For the thin soft bones found in most chickens just a pair of heavy duty scissors will work on all of the thinner bones, and a sharp heavy knife will even split the backbone lengthwise if necessary but it’s far easier to just use the knife/scissors to cut along each side of the back one through the thinner and softer ribs.

With a meat saw.