No. The only way to stop underground roots is to install a deep underground barrier and if you do this your tree will suffer greatly. Feeder roots extend well beyond the drip line of a tree. Why are you worried about those roots? Cyprus trees are propagated from seed and from cuttings. They will not send up seedlings from the roots. If you want to plant in your raised beds by all means do so. Just dig down through the roots and plant your transplants or sow your seeds as normally done. You might have to do a little extra watering at first but once your plants are growing and established there will be little if any competition between the two.
If the beds are raised they should drain rapidly. How thick or deep are the roots, 2 or 3 inches thick just below the top of the soil or have they gone much deeper
They are connected. Let's look at this from another perspective. In nature there are trees every where and they all have plants growing underneath them unless there isn't enough sunlight to provide photosynthesis. If the roots stopped growth, if they sucked up all the moisture, if they took all of the nutrients then nothing would grow. Just because your plants died previously doesn't necessarily mean that those tree roots were the cause. When you stick a transplant into the ground you are going to plant it 3-6 inches deep normally. All those matted tree roots cannot possibly soak up all the moisture and nutrients that are below them. There is something more going on than just a lot of matted tree roots blocking the growth of new plants that are added into the environment.
Ph can be a factor but soil is what it is. It is extremely difficult to change the Ph of the soil ITSELF. You can add amendments to the soil to TEMPORALLY change the Ph of the growing medium or soil but it is not permanent. Perhaps the plants that you planted were not adaptable to your soil type and/or Ph. One plant comes to mind and that is Blueberries. They will not survive in alkaline soils and if planted in alkaline soils the soil must be amended on a regular basis to ensure production and even the life of the plant. There are many others included in this. I do not believe that the roots of a Cyprus tree will affect the growing of most plants in fertile soil.
