Reducing the number of tables used - mySQL
You have 2 entities (taxes and groups) joined as M:N. 3-table structure for to store this data is optimal in most cases. Additional recommendations: 

1) declare id field in val_taxes and val_tax_groups as a primary key and alter their datatype to INT or BIGINT; 

2) remove id field from tax_mapping table structure; 

3) alter valtaxgroups_id and valtaxes_id datatype to INT or BIGINT; 

4) define (valtaxgroups_id,valtaxes_id) field combination as primary key; 

5) create foreign key references from valtaxgroups_id to val_tax_groups.id and from valtaxes_id to val_taxes.id. 

– Akina