The following script should achieve that:
# Find out which file to copy and save its name in a local text file:
# ssh allows you to specify a command that should be executed on the remote
# machine instead of opening a terminal session on it. I use this to get
# a sorted (ls -t sorts by modification date) list of all backups. I then
# truncate this list to one entry using head -1 and save the file name in a
# local file (filename.txt).
# (12.34.56.78 is a placeholder for the ip/hostname of your server)
ssh 12.34.56.78 ls -t /path/to/backups/ | head -1 > filename.txt
# Copy the backup specified in filename.txt to the tmp dir on your local machine.
scp 12.34.56.78:/path/to/backups/`cat filename.txt` /tmp/db_backup.sql.tar
# Untar the backup archive.
cd /tmp && tar -xf db_backup.sql.tar
# Import into database of choice.
mysql -u your_username -p database_to_import_to < /tmp/db_backup.sql
(This assumes that you are on a UNIX system and have scp and tar installed...)