What are the disadvantages of a delta wing biplane design?
The main benefit of biplanes is that the lift can be distributed across both wings. This provides more lift with less wingspan and places less load on each wing. Less load means the materials can have lower strength. This was very important in the early days of aviation, when engine power, materials, and weight were much more limited.

The major downside of a biplane is aerodynamics. The wings interfere with each other, causing drag. While structural bracing between the wings can reduce weight, it also adds more drag. This means that a single wing will almost always perform better, and modern materials and designs should make that possible.

A biplane configuration does not make much sense for delta wings. The main drawback of a biplane is drag, but drag increases with the square of velocity, and delta wings are best in high-speed flight. While delta wings have lower wave drag, they have higher viscous drag due to the large surface area. A second delta wing will add more area, increasing both wave drag (from the cross section) and viscous drag (from the surface).

Configuration of the aircraft also becomes problematic. Most aircraft with delta wings tend to be fairly flat, allowing lower area and therefore lower drag. The closer the wings are, the more they will interfere. The further apart they are, the more structure is needed, either in a larger fuselage or in structural braces, which increases weight and drag.