sorry for the delay, Yes it seems that packagegroup-core-x11-base removes the X11. because, in the packagegroup-core-x11-base.bb file packagegroup-core-x11-xserver and packagegroup-core-x11-utils are mentioned as dependents.
RDEPENDS_${PN} = "\
packagegroup-core-x11-xserver \
packagegroup-core-x11-utils \
So, I removed the packagegroup-core-x11-base and added only packagegroup-core-x11-xserver and packagegroup-core-x11-utils, then it worked.
here is the modified part of my local.conf file.
PACKAGE_EXCLUDE = "matchbox-wm matchbox-terminal matchbox-session-sato matchbox-session matchbox-desktop-sato matchbox-desktop matchbox-keyboard packagegroup-core-x11-base packagegroup-core-x11-base-dev packagegroup-core-x11-sato"
IMAGE_INSTALL_append = " packagegroup-core-x11-xserver"
IMAGE_INSTALL_append = " packagegroup-core-x11-utils"
IMAGE_INSTALL_append = " xterm"
IMAGE_INSTALL_append = " xclock"
IMAGE_INSTALL_append = " xprop"
IMAGE_INSTALL_append = " dbus"
IMAGE_INSTALL_append = " pointercal"
IMAGE_INSTALL_append = " twm"
IMAGE_INSTALL_append = " mini-x-session"
IMAGE_INSTALL_append = " liberation-fonts"
INHERIT += "rm_work"