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 wikipedia article, 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.
