Relational Design - Multiple tables into one foreign key column?

I think you are looking for a subtype/supertype construct. Meat would be your migrating key and would contain a Type field that indicates which sub-type of meat it relates to. So:

PurchaseMeat = Meat = {MeatBeef, MeatPork, MeatPoultry}

Where Meat is the type and the key of the subtype.

In Crow's feet notation this is a circle with a line under it.

I wouldn't create other tables for the different kind of meats. I would create meat types and cut types and then use FKs to tie them all together. Sample DB below:

USE MEAT
CREATE TABLE [dbo].[MeatCut](
[MeatCutID] [int] NOT NULL,
[Description] [varchar](500) NOT NULL,
 CONSTRAINT [PK_MeatCut] PRIMARY KEY CLUSTERED 
(   [MeatCutID] ASC))

GO
CREATE TABLE [dbo].[MeatType](
[MeatTypeid] [int] NOT NULL,
[Description] [varchar](500) NOT NULL,
[usda_beef_grade_id] [int] NOT NULL,
 CONSTRAINT [PK_MeatType] PRIMARY KEY CLUSTERED 
(   [MeatTypeid] ASC))

CREATE TABLE [dbo].[MeatProduct](
[MeatProductID] [int] NOT NULL,
[MeatTypeID] [int] NULL,
[MeatCutID] [int] NULL,
 CONSTRAINT [PK_MeatProduct] PRIMARY KEY CLUSTERED 
(   [MeatProductID] ASC)) 
GO

CREATE TABLE [dbo].[meat_purchase](
[PurchaseID] [int] NOT NULL,
[purchase_details] [varchar](4000) NULL,
[MeatProduct_id] [int] NULL,
CONSTRAINT [PK_meat_purchase] PRIMARY KEY CLUSTERED 
(   [PurchaseID] ASC)) 
GO
ALTER TABLE [dbo].[MeatProduct]  WITH CHECK ADD  CONSTRAINT [FK_MeatProduct_MeatCut] FOREIGN KEY([MeatCutID]) REFERENCES [dbo].MeatCut] ([MeatCutID])
GO
ALTER TABLE [dbo].[MeatProduct] CHECK CONSTRAINT [FK_MeatProduct_MeatCut]
GO
ALTER TABLE [dbo].[MeatProduct]  WITH CHECK ADD  CONSTRAINT [FK_MeatProduct_MeatType] FOREIGN KEY([MeatTypeID])
REFERENCES [dbo].[MeatType] ([MeatTypeid])
GO
ALTER TABLE [dbo].[MeatProduct] CHECK CONSTRAINT [FK_MeatProduct_MeatType]
GO
ALTER TABLE [dbo].[meat_purchase]  WITH CHECK ADD  CONSTRAINT [FK_meat_purchase_MeatProduct] FOREIGN KEY([MeatProduct_id])
REFERENCES [dbo].[MeatProduct] ([MeatProductID])
GO
ALTER TABLE [dbo].[meat_purchase] CHECK CONSTRAINT [FK_meat_purchase_MeatProduct]
GO