In this paper, we propose a practical integrated sensing and communications (ISAC) framework to sense dynamic targets from clutter environment while ensuring users communications quality. To implement communications function and sensing function simultaneously, we design multiple communications beams that can communicate with the users as well as one sensing beam that can rotate and scan the entire space. To minimize the interference of sensing beam on existing communications systems, we divide the service area into sensing beam for sensing (S4S) sector and communications beam for sensing (C4S) sector, and provide beamforming design and power allocation optimization strategies for each type sector. Unlike most existing ISAC studies that ignore the interference of static environmental clutter on target sensing, we construct a mixed sensing channel model that includes both static environment and dynamic targets. When base station receives the echo signals, it first filters out the interference from static environmental clutter and extracts the effective dynamic target echoes. Then a complete and practical dynamic target sensing scheme is designed to detect the presence of dynamic targets and to estimate their angles, distances, and velocities. In particular, dynamic target detection and angle estimation are realized through angle-Doppler spectrum estimation (ADSE) and joint detection over multiple subcarriers (MSJD), while distance and velocity estimation are realized through the extended subspace algorithm. Simulation results demonstrate the effectiveness of the proposed scheme and its superiority over the existing methods that ignore environmental clutter.