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.

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.