Friend, I guess you have not found the hidden 'Rest' section for players: the same for spring training as well as the regular season.
Go to the Manager Section and click on Line Up. You get the selected Line Up (headed on a black line) and below that the Bench (headed on a black line) guys. At the right-side end of that black line is a box "Open Rest Section". Click on that and below the bench listing is a new black line with "Rest". Just toggle the players in/out of there as you do to adjust the main line-up. I use it all the time for short time injuries that don't justify putting somebody on the DL and, usually later in the season, when somebody is showing a bit of fatigue.
Note, however, that if you want a player rested (maybe permanently for ST) you need to do this procedure on all four line ups (vs L no DH, vs R no DH, vs L with DH, vs R with DH). Putting a player on the DL gets them taken out of all four categories in one go. Once ST is concluded, players go back to their respective levels. If you let the AI run the minor teams it will sort out those from the rest section; in the ML you have to do it when setting your preferred big league lineups and rotation/bullpen.
If you have a player/pitcher at ST from any level below ML who you don't want to come in to any further ST games that season, just go to Roster Management, find the level, check box the guy(s) concerned and deactivate them. Only "active" listed players/pitchers can be called in to the ST squads. Even a 40-man rostered AAA (and lower level) guy who is not 'active' won't get a chance.