There are three different save slots in Iron Marines Invasion. You can delete your progress in any one of them, but your Heroes, Items, and Credits will remain. To do so, follow these steps: 

Deleting progress in a save slot

From the Main Menu, tap START to see all your save slots.

Find the save slot you want to restart your progress at, and select the Trashcan icon

A confirmation message will pop up, tap YES if you wish to proceed.

The save slot will revert back to level 1.