Remove the extension of a filename, using POSIX's built-in script only.

POSIX_path_demo.sh

#!/usr/bin/env sh
# Remove the extension of a filename, using POSIX's built-in script only.
# https://stackoverflow.com/a/63970495/4789973
path=this.path/with.dots/in.path.name/filename.tar.gz

# Get the basedir without external command
# by stripping out shortest trailing match of / followed by anything
dirname=${path%/*}

# Get the basename without external command
# by stripping out longest leading match of anything followed by /
basename=${path##*/}

# Strip uptmost trailing extension only
# by stripping out shortest trailing match of dot followed by anything
oneextless=${basename%.*}; echo "$oneextless"

# Strip all extensions
# by stripping out longest trailing match of dot followed by anything
noext=${basename%%.*}; echo "$noext"

# Printout demo
printf %s\\n "$path" "$dirname" "$basename" "$oneextless" "$noext"

Output:

this.path/with.dots/in.path.name/filename.tar.gz
this.path/with.dots/in.path.name
filename.tar.gz
filename.tar
filename