To just extract first line:
Bash (replace tabs):
( IFS=$'\t' read -ra cols <file; echo "${cols[@]##*/}" )
- load first line of file into array, columns delimited by (any number of) tabs
- print array after stripping longest prefix that ends with a slash from each element
Bash (retain tabs):
(
    shopt -s extglob
    IFS= read -r cols
    echo "${cols//+([!$'\t'])\/}"
) <file
Sed (replace tabs):
sed -E 's|[^	]+/||g; y|\t| |; q' file
Sed (retain tabs):
sed -E 's|[^	]+/||g; q' file
If the intention is to also retain the whole file as tsv:
Bash: append cat after echo in the "retain tabs" version:
(
    shopt -s extglob
    IFS= read -r cols
    echo "${cols//+([!$'\t'])\/}"
    cat
) <file
Sed: prefix s command with 1 and elide the q from "retain tabs" version:
sed -E '1s|[^	]+/||g' file