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After a series of upgrades, the High Luminosity LHC (HL-LHC) will have an instantaneous luminosity of 5-7 times larger than the LHC design value. The readout electronics of the ATLAS Tile Calorimeter (TileCal) will undergo a substantial upgrade during the Phase-II upgrade to accommodate the HL-LHC requirements. After the Phase-II upgrade, the TileCal detector signals will be digitized by on-detector electronics and transferred to the the TileCal PreProcessors (TilePPr), which is a part of the off-detector electronics. In the TilePPr, the digitized data will be stored in pipeline buffers and be packed and readout to the Front-End Link eXchange (FELIX) system upon receiving a trigger decision. At the same time, the energy information will be reconstructed from the detector data and transferred to the Level-1 Calorimeter Trigger (L1Calo) system in different granularity for every bunch crossing. The TileCal Demonstrator is designed to evaluate the performance of the TileCal with new readout electronics without compromising the present data taking. This contribution describes in detail the data processing and the hardware, firmware, software components of the TileCal Demonstrator system, together with the results of beam tests performed at CERN.