The issue with sand is proportion and the degree to which you mix it with the clay. The best soil there is, sandy loam, is a mixture of sand, silt, clay, partly decomposed organic matter, and fully composted organic matter. A little sand won't help. You need a lot of sand and then till only some of the clay up into it (but mix well). The organic matter is very important too as this is what holds the moisture. Good soils drain quickly, yet the organic matter is what retains moisture for the roots to draw on.
Adding freshly cut woodchips or sawdust will cause most of the nitrogen to be initially depleted from the soil. After decomposition is well under way, the level may recover some. If you add sawdust or wood chips, mix in nitrogen at the same time to prevent this effect. Adding some partly decomposed matter and some fully composted matter is preferable.
You really should consult your local Soil and Water Conservation agent/County Extension agent. Some other factors to consider are the parent rock of your topsoil, the pH, the composition of your subsoil, etc. In some places there is a layer of hardpan below the clay topsoil and sand below that. When other factors are favorable and the sand not too deep, using a backhoe to lift and mix the various layers can work wonders. These are things your local agent will be able to advise you about as he will be knowledgeable about all these conditions for your area. As others have said, many grasses can grow well in clay and you may not need to amend as much as you think. Establishing appropriate drainage could actually be a bigger consideration.