Can I connect a 70 amp sub panel to a 40 amp 240 breakers?
Yes, that's fine.  The breaker in the main panel needs to protect the wiring to the subpanel.  

Obviously, a 70A panel will not be damaged by 40A of power. 

Just one word; don't penny-pinch when buying panels.  Buy the biggest panel  you possibly can, so  you can add circuits later.  A 40A/240V panel can support as many as 10 or more 120V/15A circuits, presuming they won't all be heavily loaded at the same time. You might even be able to upgrade the power feed later.  Many panels are sold as 4 spaces/8 circuits. Don't count on the second one, given today's requirements for GFCI and AFCI which don't fit in half spaces.