A common way is to differentiate between two different modes of interaction is tapping vs. holding. A short tap could mean interaction while holding down on the object starts the destruction process.
Another option might be to use gestures like dragging. Drag gestures are usually associated with moving. Mining a block in Minecraft moves it from the world to the player's inventory. So dragging the block from the world into the inventory bar could be a gesture for mining. Simliarly, dragging from the inventory bar into the world could be a gesture for placing blocks.
One thing a mouse can't do but a touchscreen can are multi-touch gestures. A two-finger pinch is associated with zooming while a two-finger turn is associated with rotation. But neither make much sense for this scenario. Another way to use two fingers is to have one finger determine the context of the other. Have a number of icons at the edge of the screen which represent different modes of interaction. The player places one finger on the icon and then performs the action with the other. The drawback of using multi-touch gestures is that it is no longer possible to play the game one-handed. The user either needs to put the phone down or hold it with one hand while playing with the other.
Another thing some touchscreens can do is pressure-sensitivity. You can differentiate between pressing lightly and pressing hard. But keep in mind that not all low-end smartphones have pressure-sensitive touchscreens (or at least none which are very good). Also, different manufacturers have different ideas of how much pressure translates to which input value.