How to save a table in a server and not a player?

Datastores are not limited to just players. In fact, you can make the key of a datastore any string you want. However in this case, I would make a data store wherein the keys are player ids (don't use player names!) and the values are bools indicating whether or not the player is banned.

local DataStoreService = game:GetService("DataStoreService")
local BannedPlayersStore = DataStoreService:GetDataStore("GameData")

function banPlayer (id)
    local success , errorMsg = pcall(function()
        BannedPlayersStore:SetAsync(tostring(id) , true)
    end)
    if not success then
        warn("Failed on SetAsync(.."id.." , true) to BannedPlayersStore")
        warn(errorMsg)
    end
end

function removeBanFromPlayer (id)
    local success , errorMsg = pcall(function()
        BannedPlayersStore:SetAsync(tostring(id) , false)
    end)
    if not success then
        warn("Failed on SetAsync(.."id.." , false) to BannedPlayersStore")
        warn(errorMsg)
    end
end

function isBanned (id)
    local success , banned = pcall(function()
        return BannedPlayersStore:GetAsync(tostring(id))
    end)
    if not success then
        warn("Failed on GetAsync(.."id..") to BannedPlayersStore")
        warn(banned)
        return nil
    end
    return banned
end

game.Players.PlayerAdded:Connect(function(player)
    if isBanned(player.UserId) then
        player:Kick("You cannot join because you have been banned.")
    end
end