What is the meaning of "一把把" on "他更是一把把她的书包给枪了过去“？
The 一把把 here is made up of two different grammatical units:

The first 一把 is the classifier you mention. It is used to modify the action, and means something like "with one grab". It emphasizes that the action happened suddenly. Here are some examples from news websites:


  乘客 一把 拉开飞机安全门
  A passenger opened a plane's door with one grab.  
  
  男子欲跳楼好友 一把 拉回去
  As a man wanted to jump off a building, his friend pulled him back with one grab  
  
  走进人家客厅 一把 抢走手机
  Walking into someone's living room, [he] stole a cell phone with one grab  


The second 把 is just the normal marker for the verb's object when it comes before the verb:


  他 把 书包抢了
  He stole the book bag


So 一把把 is not a grammatical unit here, it just happens that two parts of the sentence put two instances of the same word together:


  他 一把 抢了书包
  他 把 书包抢了