Can I make stone tools able to break iron?

One of the multiple features of Iguanas Tinker Tweaks is the Pickaxe Mining Level Boosting. You can find here everything that is added/changed by Iguanas Tweaks, but the important here is this one :

Every Tinkers' Construct pickaxe start with 1 harvest level less, therefore have to be "mining leveled up" to reach full effectiveness.

This mean that, while you are mining, your pickaxe gain xp for the mining level like they do for regular levelups. Once your got enough xp, your pickaxe gain the mining level "boosted" which mean that you can mine blocks of the higher tier.

The fact here is that the "boosted" mining level of stone pickaxe is copper. So, to be able to mine iron, you will need to change the head of your stone pickaxe to a copper head using the tool station. Be aware that when you change the head of a pickaxe, you lose around 5% of your minion level xp. You will need to gain xp once again to get your pickaxe to the iron mining level.

Last think you have to know is that stone pickaxe where disabled for a reason... Your usually never need to craft one, you should craft a flint pickaxe. Here is the normal material progression from Iguana Tweaks with thier respective boosted mining level :

Material             | Mining level
---------------------|-------------------
Wood                 | Stone
Flint                | Copper
Copper               | Iron
Iron                 | Tin
Bronze               | Redstone (Diamond)
Add diamond modifier | Obsidian
Alumite (Obsidian)   | Ardite
Ardite               | Cobalt
Cobalt               | Manyullyn
Manyullyn            | Manyullyn

As vanilla tools are disabled by Iguanas Tweaks, make sure to use Tinkers' Construct tools. If you don't know how to build them, here is the link to the Wiki : http://tinkers-construct.wikia.com/wiki/Tool_Crafting