By default Google will automatically remove a domain penalty in certain period. But if the algorithm mechanics, redetect the spammy links, it is possible to penalty again.
1. In Google webmaster, there is a tool Disavow links to remove spam links, however if the volume is huge you may not able to report one by one.
2. Contact site owner to remove those backlink
3. If those link is point to subpage, you may use robots txt to no index the page, so that the robots stop index on the particular page and stop extend damage to root domain.