I'm building a Deck. Is it cheaper to buy wood from a mill rather than a box store like Home Depot?
Most mills do not produce and sell treated wood rated for contact with the ground, so any wood in your deck that will be in contact with the ground should be treated, and gotten wherever it is to be got. 

Buying wood from a mill is often cheaper, though it is not always. A smaller operation with a smaller economic influence (like most mills open to the public) will feel fluctuations in the supplies and prices of the commodities they consume in the production of lumber (fuel, electricity, trees, etc.) sharply, and so the price of their own offered commodity (lumber...) will vary sharply according to these fluctuations. A larger corporation like The Home Depot, Lowes, or Menards, likely has multiple sources for the commodities they need, they have bigger and deeper lines of credit, and a huge buffer of stock not on the shelves, insulating them from small localized changes in economies, so their prices will be more stable over the long term.

So the advantages to buying lumber from a mill that you can really count on are customization of lumber dimensions, greater choice of species of wood, and personalized service. The disadvantages vary by mill and your own preferences: is the wood air dried, kiln dried, or not dried at all and sold green? Is the wood graded by the sawyer? Is the wood sold rough cut or has it been planed? 

The advantage to buying lumber from a box store is that although they might sell an average generic lumber, this average generic lumber is always there, every day, at a reasonably average price, and you don't have to call ahead, place an order, or make an appointment, you can write a check or use a credit card, and they are often open earlier in the morning and later into the evening. The disadvantage is that the experience of buying lumber from these places is often just as bland and lifeless as the lumber they sell.

Either way you go you might save money, and you might spend more. If saving money is the crux of the issue, compare quotes and go with the cheapest. If saving money is not the crux of the issue, call your local sawmill and make friends with them. You won't regret it. Your deck wood will look and feel unique because it will be, it will have a good story to go along with it right off the bat, and, if you ever get really ambitious you'll have a place to bring logs from trees you've chopped down for sawing into lumber that you can call your own. ;-)