How to get a variable's value, then clone it???

If blockValue is the name of your block inside TemplateFolder that you want to clone, you need to find the block and then clone it. That is what the following code does:

local blockInFolder = TemplateFolder[blockValue.Value]

if(blockInFolder)then local newBlock = TemplateFolder[blockValue.Value]:Clone() end

Replace line 11 with the following code above.

[EDIT]: My bad, make sure you have the rest of the code changing newBlock in the same scope(area) as where you made the new block variable.

    local rs = game.ReplicatedStorage
local event = rs.GrassPlace
local current = workspace.CurrentBlock
local TemplateFolder = game.ServerStorage.TemplateBlocks
local blockValue = game.ServerStorage:FindFirstChild(current.Value)

current.Value = "Brick"

function place(plr,target,blocktype)
    if current then
        local blockInFolder = TemplateFolder[blockValue.Value]

        if blockInFolder then
            local newBlock = TemplateFolder[blockValue.Value]:Clone()
        newBlock.Parent = workspace.Blocks
            newBlock.Size = Vector3.new(4,4,4)
            newBlock.Anchored = true
            newBlock.Name = current.Value
            newBlock.CFrame = CFrame.new(target.Position) + Vector3.new(0,4,0)
            newBlock.Parent = workspace
        end


    end
end

event.OnServerEvent:Connect(place)