You can't do that, as Gerry Myerson has pointed out.

If you want a way to break down the computation, though, go back to one of the formulas for it:

$$ r_{xy} = {n \sum_i x_i y_i - \sum_i x_i \sum_i y_i \over \sqrt{n \sum_i x_i^2 - (\sum x_i)^2} \sqrt{n \sum_i y_i^2 - (\sum_i y_i)^2}}. $$

(See the <a href="http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient">wikipedia article</a>, under "mathematical properties".) 

So you just need to know $n, \sum_i x_i y_i, \sum_i x_i$ and $\sum_i y_i$ for the whole data set. And these will just be the sum of the corresponding quantities for each subset.