Reset Progress

Steam

In the menu option you can select a few different options:

"DROP A RANK" 

Reduces your rank by one. If you wish to drop several ranks, you'll have to use this option multiple times. Ranking down will lock items (weapons/customization) which has previously been unlocked by levelling up. Unlocked achievements will not be affected.

"RESET RESEARCH POINTS" 

Sets your research samples and points to zero. It won't actually reset/refund the upgrades of your stratagems and weapons.

"RESET UNLOCKS" 

Locks back the stratagems you get by clearing planets. This will also reset all upgrades for these items.

"RESET ALL PROGRESSION" 

Pretty much wipes your save clean. Item unlocks, item upgrades, research samples/points and player XP is reset.

PlayStation

PS Vita

You can't delete saves without uninstalling the game.

PS3

You can delete just the general save, forcing you to look at the intro and drop into the tutorial the next time you start the game, but there should be another save file that holds your progress.

PS4 

There is no permanent way of resetting your progress since you can't delete only the general save - it would have to delete all progress. 

If you are fine with deleting all progress you can play offline, but xp and unlocks etc. are stored on PSN so as soon as you go online your progress will be restored.