What is the spatial reference you are using? What data are you referencing in your clip and ship?
I am not sure if I understood your question completely on the "drawing a similar polygon on my map using the javascript API".
Any chance you can post some sample coordinates from ArcMap (plus the data frame's coordinate system) and what you get in the Javascript app? My guess is either a feet vs meters issue and you're using state plane, or more likely, the web app is ending up in "web Mercator" aka EPSG:3857 / Esri:102100.
Melita
Here is the coordinate system information from ArcMap:
Pennsylvania Polyconic
Projection: Polyconic
Central_Meridian: -77.750000
Latitude_Of_Origin: 40.925000
Linear Unit: Meter
NAD 83
Datum: NAD 83
Here is the polygon information.
From ArcMap: [[102893.542, -40718.736], [184385.372, -117977.224], [26693.39, -106864.701], [102893.542, -40718.736]]
From Javascript: [[-8519849.423608808, 4946710.14057987], [-8415589.317027876, 4843061.530225221], [-8621357.797171494, 4861406.417013655], [-8519849.423608808, 4946710.14057987]]
The map's spatial reference in the javascript app is wkid 102100.
You are using different CRS in ArcMap and a different CRS in your Javascript same application. You can try changing the data frame properties in your ArcMap to use the same (Web mercator i.e. 102100)