How to connect mouse.Target to a remote event?

You are trying to fire a mouse target, which is OBVIOUSLY not a remote event. It can result in errors and next time check the most obvious things first. In local script change the entire script to

local UserInputService = game:GetService("UserInputService")
local ReplicatedStorage = game:GetService("ReplicatedStorage")
local RemoteEvent = ReplicatedStorage:WaitForChild("RemoteEvent")

UserInputService.InputBegan:Connect(function(input, gameProcessed) 
	if input.UserInputType == Enum.InputType.MouseButton1 then
		RemoteEvent:FireServer(game.Players.LocalPlayer:GetMouse().Target)
	end
end)

and change the server script to

local ReplicatedStorage = game:GetService("ReplicatedStorage") local RemoteEvent = ReplicatedStorage:WaitForChild("RemoteEvent")

RemoteEvent.OnServerEvent:Connect(function(player, mouseTarget) mouseTarget:Destroy() end)