Remove matched item from array of objects?

What you are not grasping is that Array is a struct and therefore is a value type. It cannot be mutated in place the way a class instance can be. Thus, you will always be creating a new array behind the scenes, even if you extend Array to write a mutating removeIf method.

There is thus no disadvantage nor loss of generality in using filter and the logical negative of your closure condition:

myArr = myArr.filter { $0.name != "Def" }

For example, you could write removeIf like this:

extension Array {
    mutating func removeIf(closure:(T -> Bool)) {
        for (var ix = self.count - 1; ix >= 0; ix--) {
            if closure(self[ix]) {
                self.removeAtIndex(ix)
            }
        }
    }
}

And you could then use it like this:

myArr.removeIf {$0.name == "Def"}

But in fact this is a big fat waste of your time. You are doing nothing here that filter is not already doing. It may appear from the myArr.removeIf syntax that you are mutating myArr in place, but you are not; you are replacing it with another array. Indeed, every call to removeAtIndex in that loop creates another array! So you might as well use filter and be happy.

Apple had added what you want in Swift 4:

var phrase = "The rain in Spain stays mainly in the plain."
let vowels: Set<Character> = ["a", "e", "i", "o", "u"]
phrase.removeAll(where: { vowels.contains($0) })
// phrase == "Th rn n Spn stys mnly n th pln."