Use scoreboard teams join Blue @r[team=!Blue],
You just had the syntax a little bit wrong.
For 1.13 and above: team join Blue @r[team=!Blue]
The answers you are looking for can be found on the Minecraft Wiki entries for scoreboard and commands.
Setting up teams
To assign a player to a team you have to set up the teams first, using
/scoreboard teams add <team> [display name]
/scoreboard teams option <team> color <value>
<team> is the name of the team, e.g. red or blue. [display name] is an optional longer name, used in the scoreboard display, e.g. Team Ocelot or Team Jacob. The second command sets the team color, use [tab] after color to see your options, e.g. red, blue.
The command to assign someone to a team is
/scoreboard teams join <team> [players]
I suggest using simple pressure plates at the cave entrances, with the command blocks right below. You can then use @p fpr [players] to select the nearest player, who is normally the one that triggered the plate. Alternatively, you can use @a[r=X] to assign everyone in an X block radius sphere around the command block at once, or specify a block range with the selectors x, y, z, dx, dy and dz.
Teleport by team
To teleport every player on a specific team, you can use the @a selector with the team specifier, i.e.
/tp @a[team=<team>] <x> <y> <z>
Best Answer
If you want to have 2 separate teams on the scoreboard, create an objective for your scores, I'll use "score" in this example with the command
/scoreboard objectives add score dummy Score. Then to test it, do/scoreboard players set Blue score 1, and set the display tosidebar. Then, keep your old objective, and have a clock with command blocks testing for/testfor @a[score_ocelotKill_min=1,team=red]and one for blue, with comparator output to a command block with /scoreboard players add Red score 1` or Blue. It's a bit confusing, but it works.EDIT: Use 2 command blocks with
score_ocelotKill_min=1andscore_wolfKill_min=1to have an ocelot or wolf. Don't forget to actually setup the scoreboard objectives with/scoreboard objectives add ocelotKill stat.killEntity.Ozelotor/scoreboard objectives add wolfKill stat.killEntity.Wolf