Is it possiple to discharge the positive charge only from a capacitor and maintain the negative charge?
No. A capacitor only has one charge. The charge creates a voltage differential to the capacitor. From the positive pin, the voltage is negative towards the other pin. From the negative pin, the voltage is positive towards the other pin. What you suggest would mean that there would need to be 3 pins and two capacitors.

It would help a little if you would tell us what you are trying to do, exactly. If you are trying to make a negative voltage, that can be done by switching to which nets the pins of the capacitor is connected to. Let's say you need to generate -5 volts from +5 volts. You can charge the capacitor between the +5V net and ground, then disconnect the capacitor, and then connect the + pin of the capacitor to the ground. The - pin of the capacitor now has -5 volts, when compared to ground.

As you discharge the capacitor, the voltage at the - pin will change towards the ground; from -5 volts to -4 volts, from -4 volts to -3 volts and so on. So you will need to switch the way the capacitor is connected again, and charge it from between the +5 volts and ground. This system is called a "charge pump".