Is there a way that I can clear/expire a page cache from another page/class?

No, not easily unless you use the output cache APIs on Response.Cache and take advantage of the Response.AddCacheDependency() to make the page dependent on a common key.

Then, from the other page or class you could invalidate the common key which would enforce a dependency eviction (since the key page1 depended on changed).
Refer How to remove OutputCache by param?