It depends.
For example if your graphics hardware doesn't support DirectX 11 and is below the minimum requirements because of that, it won't work. [without major unstable tweaks]
If you graphics is technically below the minimum requirements, for example, a Radeon 7770, it will still run, however performance may not be good.
The minimum requirements are an estimation of whether or not the game is playable. However, certain things ARE REQUIRED, like Shader support, DirectX support, VRAM (sometimes), RAM (sometimes), Operating System (mostly), HDD space, CPU (some properties may be required, like x86-64 or process extension support, but raw speed doesn't).