No
Git is file based, it will not modify the contents of tracked files to derive diffs.
Possible alternatives
Remove cruft
Don't include tables/data in the db dumps that you don't care for. If it's not there creating differences, you don't need to take extra steps to ignore/correct for it.
So if for example, the problem is deleted articles that you don't want to backup, remove them from the backup process:
mysqldump -c -w "articles.deleted IS NULL" articles > backup.sql
Post process
Post process the database dump to remove things you don't care for. As an example, here's an extract from a db dump helper script I use:
#!/bin/bash
mysqldump -dRC --skip-dump-date --skip-add-drop-table --default-character-set=utf8 database $@ > schema.sql
sed -i 's/ AUTO_INCREMENT=[0-9]\+//' schema.sql
This example (for illustration only) removes autoincrement values from create table statements so that they don't generate differences in the (version controlled) schema.sql file.