Do Attacking Creatures Deal Damage Simultaneously or Sequentially?
From the Comprehensive Rules:


  510.1. First, the active player announces how each attacking creature assigns its combat damage, then
  the defending player announces how each blocking creature assigns its combat damage.
  
  510.2. Second, all combat damage that’s been assigned is dealt simultaneously.


Note that it is possible to get the sequential effect you want if you have a way of giving your Miner the ability First Strike (or Double Strike). All creatures with First Strike deal damage first, and then there is time to flicker your Miner before other creatures deal damage.