Typical cross-cut knives result in a biased cut because the blade takes time to travel while the web is moving. Serrated knife blades are fast and suitable for high speed lines, but leave a serrated cut, or something worse with tails and tears.
The two options for a square cut are a travelling knife or stopping the web to make the cut. In either case, high web speed makes the cut more difficult.
Travelling knives clamp to the web and travel longitudinally as the cut is made. The knife then unclamps and returns to the start position. I have seen these mainly in metal processing for products such as bars and pipes. The cost is high in terms of finances, complexity and real estate.
Alternately, the web can be stopped, clamped and cut while stopped. Of course the web continues to be produced and thus the material must accumulate somewhere and preferably under tension. This introduces the accumulator or festoon which takes up the web as the cut is made. Accumulation introduces a whole new set of problems such as alignment, tension control, overspeed and many other problems.