As conditions vary with every instance, it is not possible to predict exactly what would happen by cutting live home wiring. However, cutting live wiring, of any size, is dangerous as there are a number of things that can happen resulting in severe consequences. In any situation it is advisable to never cut a live wire.
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Cutting live house wiring will put you at risk for severe personal injury. Electricity could travel up tools or a loose live wire may come in contact with you. The resulting injuries can range from shocks to burns to fatal electrocution.
Any type of equipment can be damaged by cutting live home wiring. Electrical tools can be shorted out becoming irreparably damaged or even catch fire. Simple tools, such as wire cutters, can have sections melted from them rendering them unusable or they can end up welded to the wires themselves.
While cutting a live wire will likely trip the circuit breaker, there are other significant hazards. The sudden short caused by cutting live wires can cause sparks which could result in a fire or it can damage other electrical components which themselves could cause fires at unpredictable times.