You can open it, delete it, then finish reading it. The file will disappear from its folder but of course the data won’t actually be deleted until you close it.

Like this, with bash job control:

$ cat file.txt & rm file txt; fg

Or this, with shell file descriptors:

$ exec 3< file.txt; rm file.txt; cat <&3; exec 3<&-

why not just read the file, then remove it:

cat file.txt && rm file.txt

Not that I understand why you would want to do this anyway; it kind of doesn’t make any sense.

How do you mean by “remove it”? Delete the file node?

You can’t delete it before finish reading it. The most you can do is write a program to read one byte, then wipe that byte to zero.