In our community, all newspapers are recycled and collected separately from other garbage collection (but together with glass, plastic and metal recycling). They are tied up in a pile, or put together in a paper grocery bag. Is it OK to include old copies of The Jewish Press with other newspapers? I know that Shem Hashem is never written out, but there are many Divrei Torah, as well as articles about gedolim and rabbanim past and present, not to mention "Stories from the Talmud".
According to many poskim, recycling paper that has divrei Torah written on it is permissable, since this does not constitute "bizayon" - disrespect. There are also strict opinions.