One possible approach would be to copy/paste the spreadsheet content into Word as plain text (paste special) and then apply a style with 'start on new page' (format > paragraph > line and page breaks > page break before; include the required colour formatting in the style, too.

For more flexibility, though, I'd start by adding two things to the spreadsheet:
a column before the data, and an empty row between each row with content. Why? then you can add tags (for example, the colour name before a cell with coloured content and an arbitrary [empty] tag before each empty cell.

Paste special these two columns into Word, set up any coloured content styles you need (with the "break before" property) plus a plain-text style with no break before, then use search/replace on the tags to apply the styles as required.

There may, of course, be other approaches!