During the training of medical operators, forming muscle memory through repetitions is a routine path. Needle insertion is a fundamental skill that all medical staff need to master. However, such training courses often require human resources at a relatively high cost. Therefore, a needle insertion simulator for large-scale deployment and practical training is expected. In this paper, we design a passive, compliant force estimator that is low-cost, easily fabricated, and commonly demanded by needle insertion simulators. A triaxial decoupling force sensor design comprises commercial Force Sensing Resistors (FSR), soft silicon materials, and a 3D-printed connector for force decoupling. The total cost of the sensor and fabrication process is less than 5 USD. To achieve the prediction of a 3D force profile when the corresponding medical tasks are performed, we propose and compare two data-driven estimators, including least square (LS) regression and feedforward neural network (FNN). We demonstrate that FNN models outperformed the LS model regarding devised corresponding evaluation metrics. The predicted accuracy of FNN is above 90%, while the LS has a lower average accuracy of 78.02%. Finally, we test the performance of a pre-trained model on different angle gaps (15°, 30°). The force profiles of the 15°angle gap present relatively large fluctuations compared to reference with average accuracy at 84.36%. The test on the 30°angle gap has an error at 35.28%, which also shows randomness deviations from standard profiles. Therefore, the force information with a 15°or 30°angle gap can warn the trainer that an angle deviation exists from the standard setting.