Players can still see each others destroyed parts?

I'm making a mining game, and I made a pickaxe tool for this. But when one player mines a part, other people can still see this part. This is the script in the pickaxe, any idea how to fix it? It's in a local script by the way.

local Players = game:GetService("Players")
local localPlayer = script.Parent.Parent.Parent
local backpack = localPlayer:WaitForChild("Backpack")
local tool = script.Parent
local clicks = 0 


tool.Equipped:Connect(function(mouse)
	mouse.Button1Down:Connect(function()
		clicks = clicks + 1
		if mouse.Target.Parent then
			if (mouse.Target.Position - localPlayer.Character.HumanoidRootPart.Position).Magnitude < 15 then
				if mouse.Target.Name == "GrassBlock"then
					mouse.Target:Destroy()
				elseif mouse.Target.Name == "StoneBlock"then
					if clicks > 2 then
						mouse.Target:Destroy()
						clicks = 0
					end
				end
			end
		end
	end)
end)