What I mean is that on a network that uses the TCP/IP protocol (such as the Internet), an IP address is needed for hosts to communicate with each other.
So, re-reading your question...
Is there a way to design a website? with out having a IP or make it
You do not need to have an IP to "design" a website. Once that website is hosted on a web server, you of course need to have an IP assigned to that server if you want to be able to access the web site on a TCP/IP based network.
What exactly do you mean or are trying to accomplish with this statement:
Or make the website un tracebly?
Oh okay I get It now :), lol cause I want to make a website and I don't have time to study laws, and copyright stuff, I wanna make a website for example a Image Sharing Website, and don't have time to contact the publishers and asking them permission to use there photos, cause I have over 60k photos now.