Cutting tool remaining life during machining processes is essential for achieving sustainable production. Traditional prognosis methods are often crippled by the inability to adapt to diverse working conditions across the machining process lifecycle. This paper introduces a fog computing-enabled adaptive prognosis framework utilising multi-source data to address these challenges effectively. The key innovations include: (1) The proposed system integrates power and vibration data collected from LGMazak VTC-16A and IRON MAN QM200 machines. A standardised data fusion method combines multi-source data to enhance robustness and accuracy. (2) The transformer model is employed to improve prognosis accuracy of cutting tool remaining life, best accuracy of 98.24% and an average accuracy of 97.63% are achieved. (3) Finite Element Analysis (FEA) is incorporated to validate the model's predictions to validate reliability of deep learning model. (4) The fog computing optimisation mechanism based on the bees algorithm, which shows fitness value of 0.92 and convergence within 15 iterations. The proposed method reduces total data volume in cloud by 54.12%, prediction time by 33.64% and time complexity in the cloud layer by 4.62%. The effectiveness of fog computing in enhancing the operational efficiency and reliability of manufacturing systems is validated through advanced data integration and deep learning techniques.