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Assuming that the garden dirt that consists mainly of: leave, grass, twigs and flowers it will sure be much lighter than a ton if it's drain waste (mainly liquid stuff) it will be ~1 ton.  
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one cubic yard is a volume measurement consisting of one yard wide by one yard high by one yard deep. one ton is a weight measurement meaning two thousand pounds. i hope this helps you

Generally, I figure one cubic foot of earth (sand, gravel, organic material and moisture) at roughly 100 pounds.  There are 27 cubic feet in one cubic yard, so I would estimate this at roughly 2700 pounds, or a ton and a quarter.

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Assuming that you mean soil on which plants grow, I would remark that soil is not dirt, it is the source of life on earth.

I will present in metric terms (yard is not very different from meter) and therefore the question may be formulated: does one cubic meter of soil weigh one ton. The same question may be formulated as what is the bulk density or specific weight (sw) of soil. SW of 1 is defined as 1 cubic meter of material weighs 1 ton.

The sw of a densely packed sandy soil may be close to 2. A clay soil, containing organuc matter and well structured, would have a sw of about 1.4. A garden soil containing a large proportion of plant debris may have a sw of 1.0 or less.

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