Can I add sand from the beach to my soil?

Please don't add sand to your soil to break down the clay! You'll end up with a concrete-like soil. The best thing to add is organic matter like composted yard wastes or manures, leaves, etc. You can make your own compost or purchase from a garden center.

From the OSU Extension publication Improving Garden Soil with Organic Matter:

"Occasionally, a homeowner tries to change the basic nature of a clay soil by adding sand. Clays are well-ordered mineral structures that form extremely fine, flat particles. These particles are layered something like a messy deck of cards. The spaces between clay particles are extremely small, which is why water and air move between them so slowly. The diameter of the finest sand is more than a thousand times larger than the diameter of the largest clay particle. Sand worked into clay soils provides a surface onto which clay particles can adhere. The result is a concrete-like mixture that can be more difficult to manage than the original clay soil. No amount of added sand will change a clay loam into a sandy loam."

Any salt in the beach sand will likely get leached out and down during rains. If that salty water comes into contact with salt sensitive plants then you might have a problem. Depends on how the water moves on your property. Depending on how much beach sand you are working with, you can always rinse it. Or collect the sand in containers and let our winter rains leach the salts away.