Given the data from the question:

data = {<|Year->2014, ID->1, amt1->10, amt2->20|>,
        <|Year->2015, ID->1, amt1->20, amt2->25|>,
        <|Year->2014, ID->2, amt1->11, amt2->21|>};

We can introduce the key tot which is the sum of amt1 and amt2 like this:

<| #, tot -> #[amt1] + #[amt2] |> &  /@ data

(*
   {<| Year->2014, ID->1, amt1->10, amt2->20, tot->30 |>,
    <| Year->2015, ID->1, amt1->20, amt2->25, tot->45 |>,
    <| Year->2014, ID->2, amt1->11, amt2->21, tot->32 |>}
*)

Should we wish to drop the input keys amt1 and amt2:

<| KeyDrop[#, {amt1, amt2}], tot -> #[amt1] + #[amt2] |> &  /@ data

(*
   {<| Year->2014, ID->1, tot->200 |>,
    <| Year->2015, ID->1, tot->500 |>,
    <| Year->2014, ID->2, tot->231 |>}
*)

Given the data from the question:

data = {<|Year->2014, ID->1, amt1->10, amt2->20|>,
        <|Year->2015, ID->1, amt1->20, amt2->25|>,
        <|Year->2014, ID->2, amt1->11, amt2->21|>};

We can introduce the key tot which is the sum of amt1 and amt2 like this:

<| #, tot -> #[amt1] + #[amt2] |> & /@ data

(*
   {<| Year->2014, ID->1, amt1->10, amt2->20, tot->30 |>,
    <| Year->2015, ID->1, amt1->20, amt2->25, tot->45 |>,
    <| Year->2014, ID->2, amt1->11, amt2->21, tot->32 |>}
*)

Should we wish to drop the input keys amt1 and amt2:

<| KeyDrop[#, {amt1, amt2}], tot -> #[amt1] + #[amt2] |> & /@ data

(*
   {<| Year->2014, ID->1, tot->200 |>,
    <| Year->2015, ID->1, tot->500 |>,
    <| Year->2014, ID->2, tot->231 |>}
*)

In some situations, it might just be easiest to build the result associations from scratch:

<| Year -> #[Year], ID -> #[ID], tot -> #[amt1] + #[amt2] |> & /@ data

(*
   {<| Year->2014, ID->1, tot->30 |>,
    <| Year->2015, ID->1, tot->45 |>,
    <| Year->2014, ID->2, tot->32 |>}
*)