I just tried to use the Process.close() method and it works. Can you share your code so we can give a look to it?
Test code:
#include <Process.h>
Process p;
void setup() {
// Initialize Bridge
Bridge.begin();
// Initialize Serial
Serial.begin(9600);
// Wait until a Serial Monitor is connected.
while (!Serial);
p.begin("ping");
p.addParameter("www.google.com");
p.runAsynchronously();
Serial.println("Started");
}
void loop() {
if (p.available() > 0) Serial.println((char)p.read());
if (Serial.read() == 'C') p.close(); //if you send C it closes the ping command
delay(10);
}