Your better option here is actually sed, because it edits the stream on a line by line basis.
Try the following:
sed 's/\/.*//' foo.txt > foo_filter.txt
This tells sed that - per line - replace anything after the / with nothing. You then redirect the output to the new file with the >. You can read more from the sed manual here.
Note: because sed is greedy, you might need to specify the first slash with a 1 at the end of the command:
sed 's/\/.*//1' foo.txt > foo_filter.txt
You definitely can use awk if you have strings with multiple slashes:
awk -F"/" '{print $1"/"}' foo.txt > foo_filter.txt
The -F"/" sets the field delimiter to forward slash, and '{print $1"/"}' prints the first field followed by a slash (since it's the field delimiter, it gets removed on print and has to be re-included).