Calculating the voltage of zenerdiode
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When forward-biased (higher voltage on anode, lower voltage on cathode), a zener diode behaves just like a normal diode. It has a forward voltage drop of something like 0.7 V, with the exact voltage depending on the device, current through it, temperature and so on. Like an ordinary diode.

It's only when reverse-biased (higher voltage on cathode, lower voltage on anode) that the zener diode shows its special properties. All diodes have a reverse breakdown voltage, whereby they start conducting when a high-enough reverse voltage is applied. A zener diode is rated with a particular reverse breakdown voltage and is far more stable with it from device to device than other diodes.

And that's what you see in your circuit. When the voltage generator produces a negative voltage, the zener diode is forward biased and conducts like a normal diode. That's where your -0.7 V comes from. When the voltage generator produces a positive voltage, the zener has its rated voltage drop across it (ideal device here).

Note that a zener diode's rated reverse breakdown voltage is only a guide figure and they're not very precise or stable, as the current through them and temperature change. Always refer to a device's datasheet for details of how its reverse breakdown voltage behaves.