Joseph broke his foot and Grimm broke his left fibula in the Bucs' 17-10 loss to the Baltimore Ravens on Sunday.
"Lost them both yesterday in the game," coach Raheem Morris told reporters Monday. "That's the nature of the beast in the NFL. Look forward to the challenge of getting new players ready for those positions. Ronde is always in the mix to go back at saftey. You really don't want to move either of those guys, Aqib or Ronde, but both those guys have what it takes to go back there and play."
Grimm, son of Redskins great Russ Grimm, had seen increased playing time after being inserted into the lineup to replace suspended safety Tanard Jackson in Week 3. He had 57 total tackles and two interceptions in 11 games for the Bucs.
"He was a catalyst of making us become violent, making us physical, smart, consistent," Morris said of Grimm. "He will certainly be missed by the players, being the guy he is in the locker room."
Joseph, in his fifth season, has started 67 of 68 games in which he's appeared for the Bucs, including all 11 this season.
"We will miss (Joseph), but we will gain things from (Jeremy) Zuttah, who gives us a great role and a great body presence, smart sharp-thinking ideas," Morris said. "We are going to use Zuttah's best (traits), that's what we have to go out there and do."