The aim of the present study was to analyze the impact of cheese fragmentation and packaging on the dynamics of water–fat serum released from pasta filata cheese made from cow’s milk and its mixture with sheep’s milk. The addition of sheep’s milk reduced the amount of leachate from the vacuum-packed cheeses and did not cause as much loss of gloss as in the case of cow’s milk cheeses. This was also reflected in the microscopic images of the cheese samples. Consumers showed less acceptance of cow’s milk pasta filata cheeses than cheeses made with a mixture of cow’s and sheep’s milk (they had the same fat content, acidity, hardness, and oiling-off, but better stretching). The data describing water–fat serum release from pasta filata cheese within 24 h of unpacking was modeled with the use of the feed-forward artificial neural networks, whose architecture is based on Multi-Layer Perceptron with a single hidden layer. The model inputs comprised four independent variables, including one quantitative (i.e., time) and the other qualitative ones, which had the following states: type of raw material (cow’s milk, cow-sheep’s milk), way of sample portioning (whole, quarters, slices), packing method (vacuum packed and packed in brine).