Savilla faulted Tennant for failing to take firm stances on several issues - including whether to remove convicted felons from the ballot in the May primary - and mistakes he said her office had made in the past year.
But Tennant defended her actions, saying she has followed the law and applied it equally in her ballot decisions.
Tennant, a Democrat, has served as Secretary of State since 2008. Savilla has represented Mason and Putnam counties in the House of Delegates since 2010.
Tennant, who is 44 and married to Sen. Erik Wells, D-Kanawha, said she has worked over the past four years to make the office more transparent and accountable to the people of West Virginia.
She also said her staff has made great strides in the business and licensing division to make it easier for West Virginia businesses to make regular filings online.
Savilla, a 30-year-old Mason County resident, acknowledged the progress Tennant has made in the business and licensing division but said she has made several bad calls when it comes to elections.
He cited convicted felons Jerry Weaver and Keith Judd, who were allowed to file to run in the May primary, despite state constitutional language designed to keep felons off the ballot.
Weaver filed to run for Lincoln County sheriff but eventually bowed out before the election due to party pressure. Judd infamously garnered more than 40 percent of the vote against President Barack Obama in the West Virginia Democratic primary, despite the fact that he was behind bars in a Texas federal prison.
Savilla said Tennant should have denied Judd's request to be on the ballot and the election result made the state "the laughingstock of the nation."
Tennant pointed out that Republican Secretary of State Betty Ireland allowed Judd to run as a write-in candidate for president in 2008. Tennant said Judd legally had a right to be on the ballot, and she didn't think she had the responsibility to warn the public he was a felon.
"This is where the debate comes back and forth: What is the responsibility of the filer of candidates?" she said.
She said she didn't know how a line could be drawn between pointing out that one candidate had a criminal past while another might be delinquent on child support payments.
She said the press had a responsibility to inform voters about candidates on the ballot as well.
Savilla said Tennant should have been more proactive to introduce legislation to reform the way candidates could get on the ballot.
"What we can do is take the steps that Virginia has taken to say you have to have so many signatures to be on the ballot," Savilla said.
He also said she could have either introduced a bill or proposed amending the state constitution to prevent convicted felons like Weaver from running for local office.
Tennant countered by saying that while Savilla likes to point out things he believes she did wrong, he has not sponsored any legislation to address any of the problems he points out.