GroovyWS uses Apache CXF internally, so you should be able to use its logging interceptors to do the trick. Cutting and pasting the temperature example from the GroovyWS docs, the following test script prints both the request and response SOAP messages:
@Grab(group='org.codehaus.groovy.modules', module='groovyws', version='0.5.2')
import groovyx.net.ws.WSClient
import org.apache.cxf.interceptor.LoggingInInterceptor
import org.apache.cxf.interceptor.LoggingOutInterceptor
proxy = new WSClient("http://www.w3schools.com/webservices/tempconvert.asmx?WSDL", this.class.classLoader)
proxy.initialize()
println proxy.client.outInterceptors.add(new LoggingOutInterceptor())
println proxy.client.inInterceptors.add(new LoggingInInterceptor())
result = proxy.CelsiusToFahrenheit(0)
println "You are probably freezing at ${result} degrees Farhenheit"
See http://cxf.apache.org/docs/debugging-and-logging.html