Spaniard Tena, 26, joined Accies from Livingston in 2013 but has not played since suffering a knee injury against Ayr United in July.
Seaborne signed from Partick Thistle in August but only made 13 appearances.
"We thank both players for their service and wish them well for the future," a club statement said.

Gray's side had league wins over Coleraine, Portadown and Glentoran in a six-match unbeaten run to give them hope of avoiding relegation.
"It shows what a bit of momentum and confidence can do," said Gray after receiving the Football Writers' award.
"It reflects what the players have done but we cannot afford to dwell on it."
Warrenpoint are three points adrift of one-from-bottom Carrick Rangers, as well as Dungannon Swifts, and their next league match is at home to Ballinamallard United.
Gray acknowledged that Town's on-loan signings, like Martin Murray and Johnny McMurray from Cliftonville, had played a significant part in the team's revival.
Murray's goals have proved vital as Warrenpoint, who lost 13 games in a row earlier in the season, suddenly transformed their fortunes.
"Martin settled in quickly and has been great for us," added Gray.
"He has scored goals and has looked a threat. The challenge now is to maintain that."
Hamilton Academical have released defenders Jesus Garcia Tena and Dan Seaborne "in order to allow them to find new clubs ahead of next season".
[NEXT_CONCEPT]
Warrenpoint Town's Barry Gray has been named manager of the month for January - even though his team are rooted to the bottom of the Premiership table.