There are first starts in the backline for Joseph and wing Jonny May - replacing Matt Hopper (Harlequins) and Matt Banahan (Bath Rugby) - with Nick Abendanon in at full back for the suspended Delon Armitage (London Irish) and Ryan Lamb taking over from Freddie Burns at fly half.
Slater replaces London Irish's Matt Garvey in the second row, Nick Wood and Chris Brooker are in for Matt Mullan (Worcester Warriors) and Joe Gray, and Tom Johnson is at No.8 in place of Thomas Waldrom.
"We need to back up that performance against the Wolfhounds by getting it right away from home against Scotland this week," said England Saxons coach Jon Callard.
"The endeavour and energy we showed last week at Exeter was first class but not everything was absolutely spot on and we need to improve our accuracy and execution.
"We always planned to make changes over the course of these two games and it means there are more chances for those who've been playing well in the Aviva Premiership and in Europe this season.
"As we saw last week, Thomas Waldrom and Matt Banahan stepped back up to train with the senior squad after 80 minutes for the Saxons so the potential opportunities for this group are very clear."
Slater, 23, made 43 first team appearance for Tigers since signing from Championship side Nottingham in 2010 before being called up by the Saxons.
Joseph, 20, has already appeared 34 times for Irish and was part of the England Under 20 squad that reached last year's IRB Junior World Championship final in Italy.
The major positional talking point is in the back row where Johnson - a popular second-half replacement on his home ground last weekend - appears at No.8 at this level for the first time with Callard's enthusiastic backing.
The Saxons coach said: "Tom's versatility is a major strength and his great leadership qualities will be a big asset. He wants to play anywhere and he'll bring lots of energy to the position."
Sale Sharks full back Rob Miller and Bath Rugby prop Kane Palma-Newport, 21, will travel to Scotland with the squad as cover.
15 Nick Abendanon (Bath Rugby)
14 Ugo Monye (Harlequins)
13 Jonathan Joseph (London Irish)
12 Billy Twelvetrees (Leicester Tigers)
11 Jonny May (Gloucester Rugby)
10 Ryan Lamb (Northampton Saints)
9 Ben Spencer (Saracens)
1 Nick Wood (Gloucester Rugby)
2 Chris Brooker (Harlequins)
3 Paul Doran-Jones (Northampton Saints)
4 Ed Slater (Leicester Tigers)
5 George Robson (Harlequins)
6 James Gaskell (Sale Sharks, captain)
7 Andy Saull (Saracens)
8 Tom Johnson (Exeter)
16 Joe Gray (Harlequins)
17 Rupert Harden (Gloucester Rugby)
18 Kearnan Myall (Sale Sharks)
19 David Seymour (Sale Sharks)
20 Paul Hodgson (London Irish)
21 Freddie Burns (Gloucester Rugby)
22 Miles Benjamin (Worcester Warriors)