<Assuming this graph is accurate, is there any way from the data to ascertain which of the two measurements is cause, and which effect?

No, there isn't.

The time axis is too compressed for accurate interpolation on the critical scale of decades to centuries. The "temperature change" scale is not referenced (except perhaps in the text from which this graph was taken... and btw, where did this come from?); i.e., what does the "zero" represent? The CO2 concentration is noted "Antarctic ice core" - only one? Which one? And, since thermometers are only a couple of hundred years old, what is the source of the guesses indicated by the temperature curve? (most common is oxygen isotopes, but it doesn't say)

All that aside, there does appear to be a loose correlation between avarage global temperature and atmospheric CO2. You do have an interesting question about glaciation's effects on biomass, and there's more than just coverage to consider: for instance, how does the density and type of vegetation change in the ice-free remainder of the world? The big one, of course, still remains the oceans as carbon sink.

Taking a second look at the temperature curve: one is almost tempted to read it as one cycle, plus a bit more at each end, of the ~100kyr periodicity discussed in this Lawrence Berkeley Labs1997 press release; or, of the older theory of Milankovitch [see also this, from Science via the Academic Press.] On the other hand, there's this.

Multiple interlaced feedback loops; hundreds (thousands?) of partial differentials in a minimum of four dimensions, no variables with directly measurable values... Realistic assessment of the study itself - never mind interpreting or, worse yet, predicting - leads me to conclude that the only thing we can do is keep studying, and prepare our successors to deal with a reasonable range of aftermath conditions.