I can think of two ways to achieve this, one probably easier than the other. If you have SSAS installed on your local machine, or *can* install it locally, do this and then simply publis and process locally. Depending on your data sizing, it won't necessarily be fast but it will work.

Alternatively, if you have the XMLA script for the entire AS database, youcould put this in SSMS and, when asked to connect to a server, enter a local cub filename (e.g. C:\temp\mycube.cub) and then save and process. There's a little more to it than that, but Chris Webb has covered off how to do this with quite enough detail (google: chris webb local cube) that there's not much point in me copy|pasting that here.