Anyway to "grab" a player with a tool in a script?

Detecting click input without a tool

To be able to detect clicking inputs without a tool, I suggest you use UserInputService.

local UIS = game:GetService("UserInputService")

UIS.InputBegan:Connect(function(input, gpe)
    if gpe == false then -- checks if input is clear
        if input.UserInputType == Enum.UserInputType.MouseButton1 then -- checks if the input is a left mouse click
            print("left mouse clicked!")
        end
    end
end)

I won't go too in-depth about UserInputService as it is not your main question, you can check the wiki for more information here.

UIS.InputBegan is an event that fires whenever you send an input (like mouse clicks, keyboard button presses, etc), and it passes two arguments, an InputObject instance called input and a bool value called gameProcessedEvent.

The input argument contains Enum values that represent the information of the your input, such as UserInputType and UserInputState.

The gameProcessedEvent argument represents whether or not something got fired with the input. For example, if the input is a click, and a button or something was pressed with the same input, gameProcessedEvent would be true. otherwise, it would be false.

Grabbing people

Now your main question. What you want to do is sort of "attach" the RootPart of another character to your character's RootPart, making it look like you've grabbed them.

There are quite a few instances that allow you to attach a Part to another Part, but in this case you'd be using Welds!

All you have to do is assign the Part0 and Part1 property, and the two parts will stick together.

To make them offset from each other, you'll be assigning the C0 and C1 properties.

Let's say we have both you and your opponent's RootParts defined as variables: rootPart and enemyRootPart.

local weld = Instance.new("Weld") -- create a new Weld instance

weld.Part0 = rootPart -- set your RootPart as Part0

weld.Part1 = enemyRootPart -- set your opponent's RootPart as Part1

weld.C0 = CFrame.new(0, 0, -1) -- offset the two parts from each other, in this case we're offsetting Part1 from Part0 by -1 stud in the Z axis, which is right in front of Part0.

weld.Parent = rootPart -- parent the weld

Putting them together

Now we know how to weld the RootParts. To actually make this execute only when you've clicked, we're going to use Remotes.

Remotes will allow communicate between the client (a player) and the server.

Since user input (like clicking) can only be detected on the client (via a LocalScript), and actually applying the Welds must be done of the server (via a ServerScript) for everyone to see, we will require Remotes to connect them together.

-- LocalScript

local UIS = game:GetService("UserInputService")
local repstore = game:GetService("ReplicatedStorage")
local grabRemote = repstore:WaitForChild("GrabRemote") -- assuming the Remote is located in ReplicatedStorage.

UIS.InputBegan:Connect(function(input, gpe)
    if gpe == false then
        if input.UserInputType == Enum.UserInputType.MouseButton1 then
            grabRemote:FireServer() -- send a request to the server to grab!
        end
    end
end)

-- ServerScript

local repstore = game:GetService("ReplicatedStorage")
local grabRemote = repstore:WaitForChild("GrabRemote")

grabRemote.OnServerEvent:Connect(function(plr) -- this will fire whenever a player has fired a Remote. Also, when you fire a remote, the first argument will automatically be set to the Player instance who fired the Remote.
    local char = plr.Character or plr.CharacterAdded:Wait() -- gets the character model of the player (if it isn't there, it will wait and yield the script until it is added)
    local rootPart = char:WaitForChild("HumanoidRootPart") -- gets the RootPart of your character

    -- [hitbox detection here]

    local enemyChar = [insert enemy character model here] -- To detect characters around you, you'll need a hitbox system. once you've gotten the opponent's character model, it should go here.
    local enemyRootPart = enemyChar:WaitForChild("HumanoidRootPart")

    -- weld the two RootParts
    local weld = Instance.new("Weld")
    weld.Part0 = rootPart
    weld.Part1 = enemyRootPart
    weld.C0 = CFrame.new(0, 0, -1)
    weld.Parent = rootPart -- parent the weld
end)

For the hitbox system, I won't cover how to do it here, but I recommend using a GetTouchingParts() method of doing hitboxes. You can find the article on it here.

Hope this helped, thanks for reading!