How do I make SetPrimaryPartCFrame smooth?

An efficient and amazing method for smoothly interpolating properties is the TweenService.

TweenService supports interpolation for several different data types, including CFrame. You can access the service using:

game:GetService("TweenService");

Below I have outlined how you would use the TweenService to create the desired effect:

local TweenService = game:GetService("TweenService");

local TweenDetails = TweenInfo.new(
	1, --Time it takes to complete tween
	Enum.EasingStyle.Quint, --"Style" of the tween
	Enum.EasingDirection.Out, --Direction of the tween
	0, -- Repeat count
	false, -- Reverses after completion
	0 -- Delay in starting tween
);

local TweenProperties = {
		["CFrame"] = CFrame.new(rootPart.Position, (mouse.Hit.p*Vector3.new(1,0,1)) + (rootPart.Position*Vector3.new(0, 1, 0)))
}; -- Properties we want to tween

local Tween = TweenService:Create(rootPart, TweenDetails, TweenProperties); -- Initiate tween
Tween:Play(); -- Play Tween

Because the HumanoidRootPart is welded to all the other parts in a character, you can simply tween it instead of having to tween each individual part or trying to use the :SetPrimaryPartCFrame() method. You would want to put lines 12-17 inside of the function your event is calling. Let me know if you need additional help on how to implement this.

The TweenService is a super valuable service that can save you loads of time.

Extra Reading: Types of EasingStyles