I am going deploy grails web application to another computer. That another computer already has an apache tomcat server and a mysql server.
Do I need to install groovy on that machine where I would deploy my grails application? or other libraries? or just java?
All you need is java and a webapp container like tomcat. When you create a war file with
grails war, the war file will contain all the dependencies of your project, including all of grails and groovy. This does make the war files quite large, but they are extremely easy to deploy.