How can I delete a specific weapon from starter gear?

When you are deleting it from your StarterGear on the client, the server will not know that they were deleted and will proceed to clone the tools every time you respawn as usual. You will need to use a RemoteEvent for this. Add a RemoteEvent to ReplicatedStorage before running my snippet.

-- LOCAL SCRIPT
local Players = game:GetService("Players")
plr = game:GetService("Players").LocalPlayer
local remote = game.ReplicatedStorage:WaitForChild("RemoteEvent")

char = plr.Character or plr.CharacterAdded:Wait()

script.Parent.MouseButton1Click:Connect(function()

    local tool = char:FindFirstChildOfClass("Tool")
    remote:FireServer(tool.Name)
end)


-- SERVER SCRIPT
local Players = game:GetService("Players")
local remote = game.ReplicatedStorage:WaitForChild("RemoteEvent")

local function onCreatePartFired(player, toolname)
    local SG = player.StarterGear
    if toolname then
        local sg_tool = SG:FindFirstChild(toolname)
        if sg_tool then
            print("hey")
            sg_tool:Destroy()
        end
        
   if player.Character:FindFirstChild(toolname) then
	player.Character[toolname]:Destroy()
    end
end

remote.OnServerEvent:Connect(onCreatePartFired)