Verbal reading of 块?
First, it's not a verbal reading of 块.

Second, 一块块 could be used as adjective, adverb or a complement, meaning 'into pieces' or 'pieces of'. 

Examples(as an adjective， modifying a noun): 一块块肉，一块块面包，...

Examples(as an adverb， modifying a verb): 一块块地找，一块块地切下来，...

Examples(as a complement): "哦,把他们砍成一块块?", "灰熊的领地被公路切分成一块块";