You can deduct the mileage driven above and beyond what you would normally have driven for your main job.
In your case, all the weekend mileage (the round-trip) and a portion of the weekday mileage would be deductible expenses for your contract income.
The weekday calculation is little trickier. If your normal home-main job-home commute is 15 miles, but driving to your contract job adds 10 miles (total of 25), then you'd be able to deduct the additional 10 miles as an expense against your contract income. Basically, you get to deduct whatever mileage the contract job requires above your normal daily commute.
