Is it possible to convert common resources into a sellable form?

Common resources, such as: dirt, mud, ash, and stone, cannot be sold in the game. But can you convert these items into others through crafting which will allow you to sell them?

If this is the case it will be more beneficial to keep things like these to sell later on.

Short answer: Technically yes you can craft something out of stone that sells, but there are much better ways of generating currency than keeping low tier materials. You will pick up more coins from just slaying enemies while collecting all of this.

The only things dirt/mud are used to craft are each other and walls. All of those sell for nothing. Ash cannot be crafted into anything and is also sold for nothing.

Stone can be crafted into a whole multitude of other blocks, which also sell for nothing. Of the 34 blocks you can make, 3 of them (crystal, meteorite and sunplate blocks) can then be used to craft furniture at which point you can finally sell for coins. The majority of the furniture sells for 40-60 copper coins, but more if it requires additional ingredients. For example the beds sell for the highest at 4 silver, but the 5 silk you need to craft the bed sells on its own for 10 silver.

The only things stone can be directly crafted into that sells for coins are gem locks which sell for 1 silver, or active blocks. Gemlocks require 5 of a gem, and the gems themselves sell for 3.75 silver (amethyst) up to 30 silver (diamond and amber) each. Your only real option would be crafting active blocks, which sell for 2 silver each, needing only 1 wire and 1 stone block. Assuming you kept the stone blocks throughout your game, you will just need to farm wires from underground or the dungeon. If you are strictly gathering wires only to sell, crafting them into active blocks will net you an additional 1 silver each over selling the wires themselves. The Mechanic also sells wires for 5 silver, so if you plan on using wires at all it is better to farm them to use which saves you the cost of buying them.

Just know that you probably picked up more coins killing enemies while farming up those wires. (The average pre-Plantera dungeon enemy drops 1.3 silver coins).

If you're in the earliest stages of the game, stone can be crafted into statues and sold. It takes 50 stone to craft one Armor Statue, which only sells for 60 copper. If you've already got the stone, this might be worthwhile, but if not, you'll get money faster by fighting. Ice slimes drop 50 copper each, and are still one of the easiest enemies in the game.

If you are not in the early game, don't waste time with any of this. Use VanBuzzKill's answer, or use a more effective farming method if you really need money.