This seems to be a common problem affecting both screen and tmux when accessed using PuTTY. Please see my answer to a similar question pertaining to tmux for some insight into the issue itself. There is a potential solution provided as well as some analysis.
Mouse scrolling in vim through tmux, how to configure?
An excerpt of the link above describing the potential solution:
Potential Solution -- PuTTY
There appears to be an issue where PuTTY sends an extraneous ScrollDown event with every ScrollDown/ScrollUp event. This means that each attempt to scroll up gets cancelled out and nothing happens. Conversely, when scrolling down, each scroll event is doubled. The behavior is easy to validate by looking at the
vim scrolling behavior first outside of
tmux (where scrolling works properly), and second inside of
tmux (where scrolling up does not work, and a single attempt to scroll down scrolls twice as much).
According to the following gmane thread, the issue described above is resolved with a patch from Putty-X (https://github.com/atsepkov/putty-X/commit/bbcedf5a85ca1ccaa27005e7f7ebeb4c8a783b88):
Link to gmane thread: http://comments.gmane.org/gmane.comp.terminal-emulators.tmux.user/5498.
NOTE: I haven't validated the above solution myself, so please review the gmane thread for additional information.